It can. When a person is psychotic, he or she may become out of touch with reality. A person who is hallucinating and hearing voices, for example, may talk to him or herself. A person with paranoid delusions may build a bunker to protect him or herself. I knew a patient who ran 15 miles on a highway because he said he heard a voice telling him to do it. So the answer is: absolutely.
Often. Often psychotic patients misbehave because they are not thinking clearly. However please keep in mind that not everyone who misbehaves is psychotic.