Its never good to get into a deep relationship when your not in the right mind mentally. But i understand that having someone going through the same thing that understand exactly wht your saying and doesnt judge you can be amazing (thats why we're all HERE right?)

i'm not a parent but i did have mental health issues at 15 so i'm not trying to advise you what to do, but if i was ever in your situation i would suggest monitored meetings with the boy once they had both been out of hospital for a while and doing well, to see if they still had the same things in common.
Talk to her about the fact that a relationship based on mutual depression isnt healthy and that its more likely to last if they're both happy.
On the other hand, say she was an adult, she could have a relationship with someone who had no mental health issues, they would have no idea what she went through, the other boy would.
I know i would struggle to have a relationship with someone 'normal,'.
its difficult, but its best not to make any decisions until she is feeling a bit more stable.