To be perfectly honest and blunt, I think it depends on what you mean by "severe." I have what is considered a severe mental illness, and I'm a nurse. I wanted to go to medical school but personally didn't have the resources. However, having been side-by-side with doctors in emergent situations, I think it would be hard for me to rely on the judgment of someone who was struggling with audio hallucinations and what they were telling him. And I don't mean that to be rude or critical. Just, again, I think it would depend on the severity of the illness.

You're right, being a doctor isn't totally down to grades. Yes, there are entrance standards and you have to score well on the MCAT (what it's called in the States) but there are people I've known who have been at the lower end of that scale who were incredible clinicians. The three things you listed are important but it's just so intricate, that rapport with patients and learning to trust your judgment when it comes to their health (we have to do it just as much as a physician). There are times when I feel overwhelmed by my profession, especially when I'm not doing well in my personal life. I think that would be something to consider--how well are you able to cope with your illness, and how much does it affect you when you're not coping well?

Anyway. I wish you the best.