"is it wrong morally to date as a suicidal person?"
Just from personal experience... I don't think so, as long as you're not actively planning to go through with it. I've always had suicidal-negative tendencies from having a traumatic past, childhood. But, when I had met a partner that I felt loved me... I think it calmed down those kinds of thoughts, even if it'd still come up sometimes - because, I would never want go through with it, since I knew it'd be hurtful to my partner. So, it actually motivated or at least made me stay alive as long as I continued to be coupled with them... I'd keep trying at life, and seeing where it took me because I felt like I wasn't struggling alone at least (almost like they were my anchor). Plus, I cared about them, so I didn't want to hurt-traumatize them if I suddenly just died while we were together.
Now that I'm not really dating anyone seriously, I no longer have a reason to stop myself. Having plans to CBT, actually makes me hesitant to get involved with anyone now, because it could stall or stop me from going through with it... and I'm kinda just tired of living.
I think being truly loved can be healing.... but, you would need to be open to that kind of change in the first place. I think when someone has become totally set on CBTing no matter what though, they've already closed themselves off from others, and from recovering.