Yes, social anxiety can lead to schizophrenia. Studies show that social anxiety disorder (social phobia) is present in up to 1 in 3 persons with schizophrenia. There are 3 proposed pathways into how social phobia develops with schizophrenia. The 1st pathway involves social phobia developing first, then this triggers paranoid thinking in psychosis. The 2nd pathway involves social phobia developing concurrently with paranoid thinking in psychosis. The 3rd pathway involves social phobia developing from paranoid thinking in psychosis (Michail and Birchwood, 2009).
In summary, social anxiety can lead to schizophrenia in some people.
Reference:
Social anxiety disorder in first-episode psychosis: incidence, phenomenology and relationship with paranoia. Michail M, Birchwood M. Br J Psychiatry. 2009 Sep;195(3):234-41.