In this scenario, is it viable for a species in which all organisms are born females but turn into males after a certain age is reached to survive?
Yes. It's very viable, given certain constraints, and there are even certain, although mild, advantages. First, the female stage needs to be for a sufficiently long amount of time, especially if the species is intelligent. Intelligent species tend to wait until later in life to have children - here 'later in life' means sexual maturity after at least a few years of development. Humans in particular take an astonishing long time, which makes sense because of the way intelligence vs instincts works - intelligence is always better in the long term, and the longer you can allow for intelligence to develop, the better the species is. But I digress.
You'll need a sufficiently long time of sexual maturity, I'm thinking at least 25 years, possibly longer. (Again, this isn't strictly necessary for an unintelligent species, but it's better for an intelligent species to have a longer span of time.) After that, you'll want a transition phase where the individual isn't sexually mature while they transition and then reassume sexual maturity as an adult. Funnily enough, this requires less time within sexual maturity because at this point the species is a mature adult, though obviously, the more time, the better.
The lifespan looks like this. 0-15 - development, 15-40 - female stage, 40-45 - transition stage, 45-death - male stage. There are a few advantages to this, namely, that since everyone can perform 'double duty' when it comes to reproduction, they have twice the womb capacity as a fixed race such as ours.
That said, I'm not certain female->male is the way to go. True, it has benefits. On the one side, you get much faster access to wombs, which is very important for a developing society. In primitive societies, wombs are really important because those are what you use to get the best of all resources - new offspring. And while you're restricted by the number of wombs, all it takes is a handful of males to fill those wombs, meaning it's better to lose men than women. That's why males are the disposable gender and why they're the warriors. (Among other reasons.) Having the species develop first as women so they can give birth to offspring and then become the disposable men seems like a good thing.
On the flip side, men are also pretty important as the warrior caste, responsible for the hard work and fighting and all that good stuff. If they're busy giving birth to children until 45 (okay, you can play around with the ages, but the thought still stands), then you run the risk of having a male society which isn't really that strong or fit - and that's pretty bad! In evolution, specialization tends to beat generalization, so if you had a tribe of these male/female humans vs a tribe of male humans + female humans, I'd take the latter over the former.
That said, there's no inherit problems in this structure. I means, society is going to be very interesting because every marriage is going to contain a 30 year age gap and you'll have to do some nimble footwork to avoid mother/father-daughter incest issues, but it can work. Theoretically.