Should people being treated for mental illness be barred from the profession of psychology?

I have heard from some people that they do not feel that people who have suffered from (regardless of whether they are stable for the long term or not) should be discouraged from being a psychologist or studying psychology. This opinion has been expressed by the Dean of the College of Liberal Arts at my university. Personally, I think if someone is and has been stable and is managing their illness well then they have even more reason to choose this area of study. Because, if anything, they would understand what it feels like, to some degree. What is the general consensus of psychologists, social workers and other people working in the field of psychology?