It's quite an interesting question.
I myself, have some mental health issues. I've been suffering from depression and anxiety since I was 12. I've always been terrified of this being a deal breaker for someone I love. I used to be so certain that if they saw how I was, then they'd break up with me on the spot. So I used to hide it from anyone I was with, I never mentioned it, never saw them when I was down and had a habit of suffering alone. It wasn't a good habit.
I agree with what people have said about there being a difference between people who accept their issues and deal with them and people who deny them or refuse help.
I know for a fact that my relationship with H would not have worked out if I had kept up my past behaviour and just tried to hide it. We had some hiccups at first, when I was still struggling with letting myself be dependent on him but then we came up with specific responses for it and it was fine.
We came up with code words for how I was feeling and what sort of help I needed. Did I need to leave? Could I go home by myself? Did I need him with me?
We both described our different perceptions of what it's like when I'm down and figured out the best way to for each of us to deal with it.
Luckily, I'm on some really good meds at the moment, so most of my issues have dissolved, but I have to come off them eventually and it's nice to know that we already have plans in place.
As people have said, being in a relationship with someone with mental health issues is less about the fact that they have them and more about how they cope with them and whether they make efforts to change (and how successful their efforts are).
And I guess, like anything else in a relationship, a large amount of communication and trust is needed.