Off topic, but in my mind the answer to "free will" is obviously, boringly no.
If we are, as you've put it, a finite state machine, the fact that random inputs are possible doesn't make the machine any less deterministic.
Come to think of it, this is not off topic at all. It follows that if AI can become conscious, it means that consciousness does not contain (or at least require) free will. That's if we agree that a computer running code has no "free will" no matter how complex the code is.
Since we've got yes and no, why not get the third answer:
The question is badly posed and therefore meaningless. If the universe is deterministic, then you cannot have free-will as it is normally considered. If it is non-deterministic, then (by Bell's Inequality, if you want to throw around big terms) it is random, which is also not free-will as it is normally considered. If you have free-will, as we all feel like we do, then the universe can be neither deterministic nor non-deterministic. Something is smelly in Denmark; the question itself does not make sense in it's current form.
I am not actually an analytic philosopher, I just emulate them as a hobby.
I'll give a fourth one - it seems obvious to me the discussions conflate two things. Am I free to choose what to do - obviously yes. Is that choice determined by the state of the particles etc I'm made of - also obviously yes. Whether you call that free will or not is a question of what perspective you take on it. From a common sense legal perspective I'm making decisions of my own free will rather than someone holding a gun to my head. From the weird perspective / definition of some philosophers no. And they argue on and on instead of accepting it's different definitions applied to the same reality.
Come to think of it, this is not off topic at all. It follows that if AI can become conscious, it means that consciousness does not contain (or at least require) free will. That's if we agree that a computer running code has no "free will" no matter how complex the code is.