Answer

In principle it is forbidden for two reasons: 1. One may not eat or drink before Havdalah in general, not only on Yom Kippur. 2. Before Havdalah, the fast has not yet fully ended, and eating is forbidden because of the fast. That of course applies only on Yom Kippur.
I seem to recall that the Brisker Rav was uncertain about drinking water: according to reason 1 it is permitted, but according to reason 2 it is forbidden. In practice, the halakhic decisors disagree about this. I think there is room to be lenient, because we also recite Havdalah in the prayer, so as far as the fast is concerned it seems to have ended, and we are left only with reason 1. But that is only regarding drinking water.