Even though I work for AS, most of my friends who are pilots fly for FX (Fed Ex.) Anyway, they can drink when they deadhead as long as they obey all the relevant rules about drinking and not acting as a crewmember.

They are not supposed to drink when they are in uniform, however, some will head back to the galley and order up a Bailey's and coffee or other mixed drink and simply have it prepared out of sight of the pax.

The industry term for it is "pilots drink."

edited to add: the above info applies to the FX guys I know. I don't know how or if AS pilots do it.