But this thread is supposed to be about drinking in taverns.
The main way you're likely to do that is if you talk to a random sitter who asks you to buy him a drink. Social drinking like that could perhaps add a few points to "Leadership". Overdoing it already has negative effects - if I remember correctly, you pass out and are robbed. Perhaps also add a dialog option with the tavern keeper to allow you to buy a round of drinks for everyone in the place - very expensive, earns you more "Leadership" points, adds to the number of crew available for hire and raises their starting morale.