a/c belt and system

my car has A/C, which is not operating, but i do not use anyways. the A/C belt has broken, does this belt have another function besides the A/C system. do i have to replace it if not using the A/C, and if not do i have to replace it with something else like a bypass? or can i just forget about it altogether if i am not going to use the A/C? the A/C has not worked for years in it and my heating/defrost seems to work fine, but does the A/C belt control any of that?