Are children with schizophrenia generally shy?

Yes. Research indicates that yes, children with schizophrenia show significantly more shyness. As dr. Kwok explained, this is for many reasons, some because the abnormal thinking causes social problems. But, studies have also clearly shown that shyness in children in general does not predict much of anything later in life. In other words, a shy kid is just a shy kid, and can grow up just fine.
Some appear shy. If a child has enough symptoms to be diagnosed with schizophrenia, then he may appear shy because he avoids interactions with others. The child likely has had unsuccessful interactions with people in the past, due to abnormal thinking, trouble interpreting speech and body language, incorrect emotions, delusions, hallucinations, etc... However, shyness by itself does not suggest schizophrenia.