Most Helpful Guy
It very much depends.
That's not a useful answer, so I'll elaborate.
I have been in this type of situation before, and I ended up not dating her. Not because I wasn't attracted (I very much was) but because in this particular case she needed a true friend more than a boyfriend. I don't mean that a boyfriend is not your friend, but there's stress to a romantic relationship, and it wouldn't have been good long term. I liked her enough to put her long term wellbeing above my feelings and simply be the best friend I could. She credits my friendship with helping her, so as far as I'm concerned that was the correct decision in my case.
However (and this is a big however) The fact someone has a mental illness is not a reason not to date them unless dating them would cause more harm than good. Illness, physical or mental, is not something to drop a partner for (consider marriage vows: "In sickness and in health" - no mention of whether that sickness is physical or mental). So evaluate the situation and do what is best for the person you have feelings for.2