Technically, I don't think this is expected behavior -- you would not expect a jail guard to get drunk and share his alcohol with his prisoners.
But if you consider the circumstances, I do not think it is unexpected. Marshall Herrick is a pretty good guy. He is not like Danforth who really wants to kill people to keep his place.
But Herrick has helped kill people for no good reason and he is about to kill more of them (Tituba and Sarah Good, for example). So it makes sense that he would get drunk to sort of blot out his feeling of guilt. Finally, I imagine he thinks Tituba and Sarah Good are just sort of harmless crazy people and doesn't want to kill them for that reason.
So I think it makes sense -- he feels guilty and he feels sorry for the two who are about to be executed.