There are two main questions you will have to ask here: How intelligent and how alien?
Humans have been able to figure out the languages of ancient people from text alone without the benefit of native speakers, but this analysis hardly exists in a vacuum. First off, languages evolve and it is possible to find clues based on similarities with existing languages. Second, human languages have a lot of similarities due to the fact that, being human, we have a degree of understanding of other human cultures. Aliens might not be similar enough to understand human civilization on even a basic level.
If we're talking about aliens that are as far above us as we are above non-human animals, we can probably assume that they are as capable of understanding us as we are of understanding non-human animals - difficult, but not impossible. The problem is that the reason we can understand non-humans is often because we evolved alongside them and instinctively know, more or less, what we need to know (example: most mammals understand that "growling, making noise, and baring teeth" means "angry"). We can also empathize with animals reasonably closely related to us; we share emotions like fear, anger, and contentment, and needs like food, sleep, and shelter with many animals. Aliens, particularly the very alien aliens will not necessarily have this benefit.
The problem is that languages exist to convey information, but they only need to convey information that the listener does not already know. In other words, no human language intrinsically contains information about what an emotion is, how human social structure works, and so on. All human listeners know this already, but eavesdropping aliens might not, so they might not have the context that will allow them to start analyzing.
A good example of a complex "language" of a species that is very alien to us and also much less intelligent would be the "dance" of bees. Human scientists have figured it out, but only through intense study and with the benefit of context clues. We needed to know that bees get food from flowers, that they are eusocial animals that can be expected to help each other instead of keeping food for themselves, that they can see the sun and use it to calculate angles and distances, and that the dance triggers bees to go to a particular flower that the "dancer" had previously visited. If we had simply been focused on videos of bees dancing in their hives, with no understanding of bee social structure, goals, and their behavior before and after the dance, no amount of study would allow us to crack the code. There simply isn't enough information contained in the dance to tell us what we need to know.
So if the aliens are as high above us and as different from us as we are from bees, I would guess that they could figure out our language with enough study, but they would probably have to observe us directly to get the necessary context. Broadcasts alone, especially audio broadcasts, would not be enough.