I'm going to preface this by saying I have no experience in this field whatsoever... But if I may ask....
Does he have a history of depression (prior to the academy)?
If the answer is no, then it could just be the 'suckyness' of the situation getting to him. There was a time at OCS when I was 'depressed'. I was stuck in holding company by myself (long story but everyone got shipped out of the command) for 3 weeks. I went crazy... I had zero contact with anyone, and had NOTHING to do. It was like prison, and it took a harsh toll on me mentally at the time.
The reason I say this, is because depression meds aren't the route I think you'd want to go for this... If it's his plebe year (which others can talk to you more about), he may just be hating life because of 'the suck' that is supposedly plebe year.
As an OCS guy, I can tell you that parts of military training are tough as nails, and meant to push officer candidates to their limits, and even their breaking points.. This is normal and expected. I've never seen more grown men cry in my life than in OCS.
IF this is it, then I can tell you nothing helps more than an abundance of thoughtful letters, pictures, and care packages (depending on the phase of training) to let him know that you are behind him 100%. Nothing can put more stress on someone in a harsh, confined training environment than things being shaky at home or with the girlfriend (not that this is at all the case).
Now if he has a history of depression, or is talking about doing something stupid or scary on top of this 'normal' stuff that I talked about, then it needs to be immediately brought to his superiors and he needs medical attention.
As to the meds and the effect on the career, that is for the doctors/boards to ultimately decide...
My point being, is that if he is just hating life because the training sucks, I don't think Prozac is the route he wants to take.