As noted by Regnveir, patients on an inpatient unit who are used to residents and students probably won't be bothered by your presence. Outpatient psychiatry is a whole different ballgame though - patients are much less likely to let you sit in on their 15-30 min, once-every-howevermanymonths visit with their doc, especially if they want to talk about personal problems or are participating in therapy.
However, on an inpatient unit, you will probably find that there are group therapy sessions and other group activities that you can probably attend if you are free at those times.