I dont think there is a direct correlation between schizophrenia and mysticism in the broad since, but YmirGF makes a good point. I think I agree with you. BUT there has been research that shows a strong similarity between the schizophrenic experience and the experience of the individual chosen by spirits to be a shaman (in the strict Siberian "shaman" context, as well as ecstatic trance healers of other cultures).
One who is chosen by the spirits to be a shaman, around the late teens to early twenties (the same time frame that schizophrenia usually starts to develop strongly) has similar experiences to the schizophrenic including the hearing of voices, the intense visions that they have no control over, visual hallucinations etc. The key is that when the person in a traditional animistic society starts to have these problems, the shaman becomes aware it and starts to teach them. In this case, the initiate learns how to control the spirits and utilize his illness.
In these traditional societies, the shaman is a wounded healer, and always falls incredibly ill before being initiated and taught by an elder shaman. Often times the person will fall fatally ill without apparent cause, experience horrific visions, act like they are crazy without rational thought and etc.
The person who is to become a shaman is chosen by the spirits at birth, and when the time comes, the spirits come to this person and torture them so that they have no choice but to become a shaman. It is only once the person accepts the vocation and begins instruction that their illness goes away.
I have read about some shamans who have said that when they have not shamanized for a long time they start to become ill again. There was also a story of a shaman who stopped shamanizing, because he had been convinced that it was a sin, and became blind because the spirits took his vision away from him for giving up his duty. Ultimately, being a shaman is not a choice because, like mentioned above, the spirits choose the person, and often times it is not a desirable thing to become a shaman. So no one can decide they want to become a shaman and then become a shaman (like too many new age dimwits claim). one can learn to drum, go into trance and journey, but unless they are chosen, they can never have the power that a shaman has.
These kinds of things show a strong similarity with schizophrenia, so it would be interesting to see if a person who has been diagnosed with schizophrenia could, with the proper resources and teacher, learn to utilize this illness and actually become an ecstatic healer. I think it's only because western society has no source of knowledge for this kind of thing that we treat it as a mental illness.
Also, I have to stress the fact that "shaman" cannot be broadly applied to any traditional healer in an indigenous society. That's the fault of western anthropologists. It strictly applies only to certain tribes in Siberia. There are no "shamans" in the Americas, or Africa, or Europe. There are other proper terms for those peoples. But overall, most of them share the commonality of being a wounded healer who practices ecstatic trance, meaning they go into trance and leave their body for the spirit world as part of their healing ritual, usually using a drum.
That was much longer than I expected. Hopefully it was at least educational lol