I don't know any stats or research but I can say that when I started to wake up I realized that there were many, like myself, who suffered from depression. I don't know if they came into the religion depressed, but certainly getting the canned response to "pray and go out in service more" for every issue didn't help. Praying and going out in service didn't help my failing marriage or the fact that we always had financial issues due to shitty jobs because of lack of education or a myriad of other problems in my life. It can be incredibly frustrating and taxing on a person's mental health to be "waiting on Jah" for years instead of taking actual steps to remedy a situation.
I also feel that people feel a false sense of acceptance in the congregations when they first start studying that often attracts people with mental health issues who might feel rejected elsewhere.