I'm sure being healthy is definitely helpful for depression, but I don't think it could eliminate it. I've had major depressive disorders and bipolar and anxiety and just about everything both while I was a health nut and while i treated my body horribly. it just personally hasn't made a big enough difference.
my doctors (every single one i've been to) have said that i need to exercise and i will agree that regular exercise is really good for anxiety.
but i do think that a lot of the imbalances which cause psychological disorders need more than just good nutrition.

(but maybe i've just been brainwashed by the mental health industry whatever)