Yes, you can date someone with schizophrenia but you must know that it might not be easy. You will need to insist that the person stay on any meds and keep regular counseling and other therapy appointments or you could find yourself biting off more than you can chew. There are some things that you will need to do as well such as practice patience, have a therapy support system of your own, and not judge.
Since someone with this problem has trouble distinguishing reality from fantasy, you must not beliee everthing they say. If they tell you a martian came to their room the previous night, understand that it is the disease talking. There are many things you should know about the problem so the more you research about it, the more you will be able to decide if you have enough unconditional love to stick it out.