I would say that regardless of mood, it's still a worthwhile pursuit. Because to sometimes be unwilling to be one, whole, person is essential to finding who you are, eventually.
Once you have found who you are, you are less likely to see changing who you are as a top priority - granted that you like who you are. But it most likely took a lot of time to be who you are and during that time, it would have screwed you forever to be forced to stay who you were. Which is, I guess, why young people care about privacy. And who is to say that you will always like who you are? Which is probably why old people care about privacy.
Becoming a person in the first place has a lot to do with trying out traits or persons. I don't think Depression is necessarily a cause (although it may be) for pursuing privacy about that search, maybe it's just a symptom - that not being whole is depressing and thus searching for yourself deserves privacy. To protect your unfinished person to be finished by the outside world.
But it's also about the pressure we put on ourselves. Merlin Mann said somewhere that Procrastination is forgetting who you are for a certain period of time. I initially thought that that was an entirely negative statement. It just now occurred to me that it can be a positive statement as well. And that being depressed about not "getting things done" is entirely useless, because you're basically punishing yourself for trying harder to find out who you are (instead of finishing stuff that who you were cared about). Which stunts your development and leaves you more likely to procrastinate, kicking you back into a cycle of self loathing.