No defense of the WTBS here, but I'm not aware of any study which pits suicide rates when "treated" by professionals vs nonprofessionals is done.
People sometimes kill themselves and it's sad, but sometimes these also kill themselves while being treated by mental health professionals.
(I know 2 "worldly" guys who killed themselves and 3 JW's. The JW's were being treated by mental health professionals.)
This is not just a JW problem. If you care to help, the following resource makes some discussion of the many factors involved.
www.sprc.org/library/nssp.pdf
Yes, yes, WTBS = Bad, but it isn't 100% responsible any more than any religious group.
Take Scientologists, for example, they'll be all for getting a physical, but totally abstain from the pharmacological solutions to depression.
Christian Scientists feel prayer covers it all.
I think it's safe to say that many, many religions and religious people feel that more of whatever their religion is peddling is the answer, (but not all).