As others have said there is a difference between schizoid and schizophrenic. But I think in both cases the answer is yes. I know less about schizoid, but my roommate is schizophrenic and she definitely has empathy. She may not have the best understanding of how her actions make others feel, but she does care about it. It's just harder for schizophrenics to focus on the right issues, I think.

A true lack of empathy would make that person a sociopath.