Nah, I would group mental illness into facticity- its part of the inherently meaningless suffering that occurs in life. Its a set of cards you are dealt. Existentialism requires you to get to a point where you stop seeing yourself as a victim and not let your suffering beat you down into nihilism and living in bad faith or helplessness. Its about playing with these cards in the best way possible and living a meaningful and fulfilling life despite the brutality of reality.