Probably not allowed
Even if a pilot were to hide his alcoholism
and get an airline job, it would be hard for him to work without breaking rules.
Pilots' schedules are erratic, so an alcoholic would have to avoid drinking for long stretches of time (hard to do for an alcoholic). He can't have alcohol within 8 hours before flying, can't have alcohol while on duty, can't have alcohol level 0.04 or more if tested, etc...