I'm going to say... maybe.
Would I get into a relationship with someone who clearly had a mental illness that was left unchecked? No way in hell. Would I get into a relationship with someone who was managing their issues? Possibly, depending on other factors.
I definitely wouldn't leave my partner if he suddenly developed a mental disorder. I also wouldn't stay with him if he let it control his life.
I guess I can echo what others here have said - it all depends on how the illness is managed. I suspect that I might have BPD, but I'm able to contain the crazy for the most part. I definitely have depression and I'm working to find the right drugs for it. I take the necessary steps, so I would expect the same of anyone I wanted to start a relationship with.