I stand by the already stated issues about scientific community. The scientific community would love to learn about alien life, though this isn't limited to scientific community. There world would change the moment alien life was confirmed. An entire different question on the worlds response to alien life is required, it's too much to go into here.
Scientists will respond with the same awe, or fear, or reevaluation of religion etc that all humans will go through. They will tend to be more curious, and likely more optimistic, about the creature; less likely to be swayed by doomsday claims and other fear mongering and more focused on the questions and answers it can offer.
That is...if they know it's a creature.
From what you described they wouldn't appear, at first, to have any way of knowing that this thing was alive. It sounds like a huge moon or plantoid, not a living creature, and that's what they would be inclined to presume for awhile. After all alien life is so different that it's likely hard to recognize, through in the size and the fact that awol plantoid is a far more likely premise then alien lifeform and that's their first instinct when they see it...which by the way will be way before it enters the solar system. It would be a very unusual mass, flying in a very odd way, and thus a very important intellectual curiosity in any case, but not nearly the same as a lifeform.
If they see it as a non-lifeforms their be very curious, but more then that, worried. Something of that size coming towards us is a potential issue. First thing we would do is calculate its trajectory to see if it is coming towards earth, potentially colliding with it. If it is headed at a very different angle that would help (though it probably won't be...see evolutionary rant, and suggested changes to better justify creature while staying as true as possible to your stated form). However, even if it's not coming close to earth it can still be a threat. That much gravity can affect the orbits of things in the solar system. not by much, but Earth's orbit is a very delicate thing, just the tiny shift and we either freeze or burn to death. If that thing comes anywhere close to us, rather it strikes us or not, it officially qualifies as a very bad thing, possible even an extinction event sort of thing.
If its trajectory puts it further away from earth it's not as bad, its gravity won't be too huge so it's only if it makes close passes to any of our land masses that it's a major issue, I think. This isn't my area of expertise, a follow up question on what it would do to our solar system to have such a large mass enter it, and how its trajectory affects this, would likely be worth asking to get people who are more specialized in this area to answer.
Of course you seem to want humans to respond to a creature, not a planetoids. For this to happen lets see how we can have people identify it as sapient as soon as possible...
The best way to justify this is those radio waves (though they don't make sense entirely to me, I would modify them slightly but get to that later)
Once the scientists notice a new stellar body of interest they will turn powerful telescopes at it, including ones that will detect radio waves. Their detecting of radio waves is the best way to achieve a belief that it may be alive. If the waves are communicative they will have certain mathematical properties, properties that will suggest something interesting about it that could suggest sapience (but not confirm it yet, no one is going to figure out how to 'speak' its language to confirm intellect just form listening to it).
Now the scientists have their first debate, do the odd signals suggest sapience. Humans likely will not assume the planetoid is sapient at this time, sapient life living on (or creating) the planetoid will seem more logical...partially because I don't think your creature can evolve as stated, but even if we assume it's plausible humans will naturally think in terms of humanoid sized creatures at first; even scientists, who should know better, will likely have their innate biases suggest that. So instead the debate will be on rather lifeforms can live on the creature.
Note, some will say the signal could still be random, a odd quirk of the planetoids causing odd fluctuation of signals. In fact there are groups of humans who will resist any view of alien life and work very hard to come up with arguments against it, but even those without bias will have to weigh the absurdly low odds of signs of life coming so close to earth with the odds of odd random-but-natural modification/creation of signals. Your weighing two options that are both absurdly improbable, trying to decide which is less probable isn't exactly easy.
As the 'unknown mass' gets closer they will do everything they can to 'look' at it with our various telescope and other sources, hoping to get more detail to use to draw conclusions, remember the thing will be so far otu when first detected that we will not be able to make out much detail at first.
At this point what happens depends on two key questions.
1. How fast is it approaching us
2. Does it talk back?
as to 1, this is relevant due to the question of how we study it, and how much time we have to study it. And the answer is...lots of time.
I'm not certain how far away it will be when we detect it, astronomy is probably my weakest area of physics next to string theory, however, SETI claims to be able to detect even very weak signals from a parsec away, that's more then 3 lightyears. Now that's really a bad example, the question with seti is more about rather they are looking at the right 'place' to hear it, but at the same time this thing is much larger, much stronger signals (it kind of has to), may be intentionally broadcasting at us, and if going at all fast has doppler effects so...my limited science says that we probably will detect it from a parsec away; until someone who knows better comes and tells me I'm wrong.
I know the creature is not going to be moving at anywhere near light speed, so if it's 3 lightyears away when detected it will take it many years to reach us, we could have decades to study this. In fact if we assume the creature intentionally came to earth (see below again) then its speed will be very low due to the energy requirements. In short were going to have quite a bit of time to study from afar, and to invest effort into researching this thing.
So we would be spending money building better ways of studying this, moving our space based telescopes to study it further, send off a probe towards it, though the probe won't be getting close enough to get useful data for quite awhile either.
When trying to decide if it's life their look for a few things. What it's made of won't help, they aren't going to find liquid water for example. They will then be looking for signs of life living on the planetoids, transforming, atmosphere that could support 'life', alien-made sataliets etc, this will all fail of course. People will quickly point out that we are seeing one signal, not dozens, and any sapient species able to broadcast such strong signals would likely be broadcasting a ton of them (we sure are), so the fact that a single signal, that isn't focused enough to be intentional pinpoint communication via technology, suggests this is not done by sapient technology. Since the idea of sapient plant sized life is so absurd I don't think many will leap to that, for awhile they likely will still presume some really bizarre natural signal.
The next best indicator of life will be when they get close enough to make out the planitoid's surface and see how structured it is, not a random pockmarked collection of gravel. However, I'm not certain when we will see this, I feel like it will not be until quite some time after we detect the creature that we can view it with enough clarity to see the sort of organized structure required for life.
In any case the argument that this is an alien made probe, rather then a sapient being in its own right, is still likely to be made. Yes it's bizarre and shocking to make anything so large, but the idea of planet sized creature is so unlikely on its own that planet designed probe still seems a valid alternative by comparison. I suspect people will suggest that some aliens took an existing stray planetoids, sunk some equipment into its core, and then let it fly towards earth to protect it, as idiotic as it seems, since what more valid option is there, a planet is alive?
And for that matter the fact is even if it's on our door step (and somehow not killing us all in the process) people will still not necessarily accept it as alive. I keep referring to a "random natural occurrence" above, what is the difference between that and life? life is, ultimately, a random natural occurrence. This thing is so..well alien, that people are not going to be quick to call it alive. Lets look at googles definitions of life:
the condition that distinguishes animals and plants from inorganic matter, including the capacity for growth, reproduction, functional activity, and continual change preceding death.
2.the existence of an individual human being or animal.
Well great, by googles definition this thing isn't alive, it's inorganic. The very first definition of life I found already killed it, and the majority of definitions of life I see do this as well. However, ignoring that part, scientists look at the list of qualities in option 1 to define life generally. The problem is all of those take so long for your creature that we aren't going to detect that any of it's happening for a century or more. There are other definitions, like communication, but as I said from just listening to the signal we will know it's quite unusual but it's hard to say we will be ready to agree to life there.
To be frank without some sort of communication we may never define this thing as life while it's in our solar system (and were still not driven to extinction by it). Oh some will consider it alive, there will be a debate, but the odds are going to be with it not being, again the intelligent aliens sending radio waves from a planet sized prob explanation is still not much more improbable then planet size life, so even definitive proof of intelligence communication does not necessarily mean the alien being declared alive. Though since this would mean confirmation of alien intelligence of some sort all the really interesting things will still happen on earth.
Still, without communication this is a pretty slow moving revolation, so lets look at it communicating back. I can't really get into this without talking about how it communicates, which brings in so many other issues that...well I think it's time for that promised detour on evolution.
Now as to communication...
If we shine radio waves at it, and we will, it may very well 'hear' them, after all if it communicates with radio waves it must be able to hear them as well.
Thus it may respond to our radio waves by sending different waves of its own. It won't take long for scientists to recognize that it's radio waves change depending on what we send it, and this will switch everyone over to the possibility of sapient life existing (rather the alien is alive or just a probe programed to respond will still be up for debate).
Now we are not going to 'talk' with this alien in the usual sense, its language is going to be utterly alien and indecipherable. Thus one of two things will happen, depending on rather or not it's sapient.
If it's only sentient then its responses will be based off of some pre programed 'body language'. It hears a radio wave that it interprets as something and responds back; if it hears what it thinks is a threat it responds with its equivalent of a hiss, if it hears a welcome bark it response back to that etc. Its responses will vary depending on what we send, but it can't come up with a way to actually talk with us any more then a lion will.
This will leave the debate of sapience open longer, since while our signals cause different signals to come back there is not, at first, any understanding as to what they mean and it fails the sapience tests we send it. However, over time we will notice it response to certain messages in certain general ways and is adapting those messages (a dog may not think, but he will start barking differently to the sound of someone walking around in the next room after hearing it a few hundred times). There will be a strong push towards sapience existing, with some still arguing natural phenomenon.
Notice I said sapience, not sentience. The scientists will likely lean towards sentience that is simply too alien to understand, and thus incapable of understanding our 'sapience tests' due to simple foreignness. The possibility of an alien too inscrutable to comprehend is not that impossible with such divergent evolutions, and again for awhile they will likely still be leaning towards the moon sized probe hypotheses, which requires sapience.
With time we will eventually likely conclude it is non-sapient. this will lead to the argument about rather it is alive I mentioned earlier. Trying to declare something so foreign as alive when it is not sapient as well is just hard for people to accept. Even if declared sentient people will disagree and others call it an accede mic distinction, kind of like the debate over rather pluto is a planet, only obviously allot more personal. Since sentience takes so long to develop we probably won't get to see it become sentient; especially since we would have been so stuck in ou view of sapience that we won't notice the slow sentience developing; unless it somehow developed faster due to the unique stimuli of earth triggering it.
If it's sapient things are more interesting. We will quickly resort to the standard sapience test, MATH! (hopefully it didn't sleep through class). Were talking about sending pulses that double every second to see if it figures out the doubling and sends back the next double in the sequence, or prime numbers, or any other mathematical sequence looking for it to respond with the next patter of the sequence.
This won't be an immediate response, it could take months or longer to get a response this way, because we don't know what it's listening for. Before we can 'talk' with it we need to figure out what signals it likes. That means figuring out when we go beyond frequencies it can 'hear', figure out when we are shouting too loud and hurting its ears, or when our pitch is too low, or that were speaking so fast it can't keep up etc. There will be experimentation to figure out what its normal frequencies are. If it's sapient this actually won't take as long, but if it's non sapient it will take quite a few iterations of different ways of sending frequencies to rule out were not just talking wrong to it.
From here ...there are already questions about how to communicate with a sapient species who's language you don't know on the site for what scientists will do.
At this point most will accept sapience, though plenty will keep coming up with no true scotsman debates and moving the goalposts.
Scientists will now focus the majority of their energy in 'talking' with it, using math to create some crude quasi-language. The other big step will be to figure out if it is made or evolved thing.
From here the rest is part of humans normal response to discovering sapince, already covered on this page.
