Mention engagement for mentally disordered people in application?
Many medical research jobs require interfacing with patients, stakeholders, family members, potential study subjects, etc. Therefore, people-skills can be a great asset. Furthermore, it sounds like your friend started a support group on her own initiative and successfully ran this group for some period of time with a fairly large number of person. This speaks to being a 'self-starter', and to good organizational and time-management skills, since she was doing this will completing her degree. The volunteering aspect is not as important as the other aspects, in my opinion since volunteering usually provides evidence of being motivated/'self-starter' which creating the group already emphasizes.

My feeling would be that this is a good thing to mention as it highlights several desirable qualities. In my opinion, whether or not your friend has mental health issues is her own personal business and not that of potential employers, unless it requires special considerations, so I would advise her to describe this work without reference to her personal health situation, framing it in terms of interest rather than personal experience - i.e. her interest in mental health issues led her to create this group which she managed for a certain period of time with however many clients.