It's the other way 'round, mental illnesses cause permanent brain damage if untreated.
Actually, in the case of schizophrenia, the damage has already been caused.
Here's a quote from an article stating that brain damage in schizophrenia can begin in childhood.
"Compared to the brain scans of healthy children, scans from children with schizophrenia showed tissue loss in the sensory cortex, parietal cortex, temporal cortex, frontal cortex and supplementary motor cortex. The loss of brain tissue started in the parietal lobe and as the children grew, the damage spread to frontal and temporal areas. The amount of tissue lost in the temporal lobe was associated with the severity of symptoms (e.g., hallucinations, delusions) shown by the children."
http://www.loni.ucla.edu/~thompson/MEDIA/PNAS/nfk.html