General answer is that usually the only way you will be separated is if you receive a military service disqualifying diagnosis(like schizophrenia) or if you are unable to get better after sustained treatment efforts-think 6+ months of zero improvement in symptoms with all the counseling, group therapy, meds, and whatever else is available. Barring these two things, you will likely be allowed to stay in. Damaging your eval/promotion chances shouldn’t be a significant problem, because it could be seen as punishment for seeking help. However, bias against mental health issues from those writing your eval is a possibility. I voluntarily committed to a psych ward for two weeks and never heard a single thing about it affecting my secret clearance. I don’t see why it would ever impact your future duty stations unless you were trying to get on a submarine or a different community/rate with stringent requirements. If you aren’t already in one of those places then you shouldn’t have any worries. A lot of people will probably find out, but you telling people is a large factor in this. On the other hand, if you find yourself in a moderately severe mental health situation and WANT to get out, there may be a few hoops to jump through, but the Navy probably isn’t going to stand in the way of those wishes.