I don't find it even remotely creditable to suppose that adopting or rejecting a label can either instigate or cure mental illness. Rather, what I would expect is that mental challenges are experienced by religious and non-religious persons in roughly similar proportions by population, but that religious people are much more likely to interpret ecstatic experiences as being supernatural in character.
Is it good or bad for mental "illness" to be interpreted as a religious experience? I see both pros and cons here. If this belief leads people to eschew clinical psychiatric care, this could be a very bad thing, particularly in the case of illnesses on the schizoid or paranoid spectra that are easily controlled by medication. On the other hand, mental illness is often associated with heavy stigma in secular society, whereas religion can provide context and narrative to "abnormal" experiences, giving someone a strong sense of understanding what is happening to them and what to do about it (however much you might disagree with the scientifiic accuracy of this framing, a factor which does not affect the efficacy of such a belief) while also reducing the likelihood that others in the community will reject or isolate the sufferer. In cases of more common mental illnesses such as depression and anxiety-spectrum disorders, there is strong evidence that participation in religious communities can greatly benefit treatment, especially in cases where both modern medicines and religious counseling are being employed. People place a strong degree of trust in religious leaders, and this could conceivably have a net positive effect if it makes them more likely to seek care in the first place. Even if it is through pastoral counseling rather than professional care, therapeutic conversations are beneficial, and in the modern world most religious professionals will urge a seriously challenged individual to seek out formal psychiatric care where needed.
