Yes. The mice between the two are *almost* completely compatible.
(Short version, the very oldest Mac mice don't work on the IIc because of a minor wiring omission, but later ones do; the IIc mouse is just a later-model Mac mouse in a different color case. So if it works on the IIc should be fine on the Mac. As a reverse example, the mice that came with my 512k and Plus both work fine on the IIc.)