Do people with autism or Asperger's syndrome have a higher genetic predisposition to psychosis or schizophrenia than that of healthy people?
Generally speaking, yes; it's relatively more common for psychosis to be comorbid with or present after diagnosed Autism.
For a good overview of this topic read Autism and Schizophrenia (Yael Dvir, MD and Jean A. Frazier, MD).
Note however that the similar (but not identical) features between COS and Autism:
There's also likely a bit of sample bias going on; children presenting severe symptoms of either Autism or COS are logically much more likely to be seen by medical professionals than neurotypical children or those who may have Autism but present less significant external symptoms. So take the specific percentages with a grain of salt, but the two certainly seem to be related.