There is no evidence that they do, though this is not proof they can’t. Unless they specifically have a way to quickly metabolise alcohol, then being biological, alcohol must eventually affect them. They obviously do drink alcohol as a bottle can be seen in the reps’ apartment in Leon’s photo. This is ignoring the possibility of Deckard being a replicant, but again, although there is plenty of evidence that he drinks a lot of alcohol, it is arguable whether he actually gets drunk or not.
Posted in: 4.3. Replicants