No, but treatable. We do not have a cure for schizophrenia, nor do we seem near to one. However, many with schizophrenia can lead quite normal lives with appropriate medications and other interventions. One of the hardest parts about this and many mental disorders is that, just when a person most needs help, he or she is least likely to believe it.
More science needed. Small numbers do recover completely and need no further treatment. Looks cured... Recent data suggest very early treatment has large effect on prognosis. Again, adding to hope that more patients may be curable with early, good treatment. For most patients, we are still unable to cure. Best we can is to ameliorate their psychotic symptoms. Cognition and motivational symptoms are harder to improve.