Should person with schizophrenia have children?
that's a loaded question with many factors to take into account.  Priority in life for those with serious illness should be given to self to make sure they live a happy healthy life.  If life is already difficult more than the norm, then having children will cause even more difficulties (if self is ill and having to take care of possible ill children).  Since this a Buddhist Q and A website, I'm going to try to link that.
remember this


  "whatever brings you joy, it will cause suffering"


It comes to personal choice, if he/she decides it is a fair trade off.
As for my personal thought. No, dont risk adding more troubles to an already troubled life.