Yes, drinking in the middle of the night is common for a full-blown alcoholic who has become physically addicted to alcohol.
AW would wake up shaking for a drink in the morning . . . but if it was 1,2,3 in the morning -- bring on the vodka! Any time is a good time for a swig.
Physical withdrawal for a person like this is unthinkable and frightening, because of the risk of seizure and just basically getting incredibly ill, without a drink.
This kind of heavy use is a sign that it is going on 24/7 -- there will always be a level of alcohol present. The only times my AW was tested, her BAC was 0.35 both times, and one time blew a 0.40+ "hot" -- and she was walking and talking!
Once she reached this state of constant inebriation, whether visible to outsiders or not, the AW was heading for OWI's, getting fired for drinking on the job, drinking at inappropriate times (church, funerals, family gatherings), and all kinds of mayhem.
My wife has NEVER been able to quit on her own from this level of drunkenness; it always required an accident or trip to the emergency room, or straight to detox, for her to quit. Awful.