it depends. if the patients are on the same exact plan then generally yes. but there are so many different types of insurance policies and doctors participate with some of them and not with others. what may look the same on the surface may actually be two different health insurance policies even if they're provided by the same insurer. and a physicians' panel can become full at which point he or she may stop taking new patients.
if doctor. accepts health insurance or medicare from one patient is he obligated to so for the other patients?