I would say I was in the escape reality bracket, however I know a friend that had a relative that went to Alcoholics Anonymous, and from what they told me, the definition was when the drinking becomes a problem, eg leads to domestic incidents, social embarrassment, or danger of losing job.
This page http://www.fasting.ws/juice-fasting/fasting-for-addiction/alcohol-addiction
says juice fasting helps with alcohol addiction, so my guess is that REAL fasting, i.e. water fasting, would help. I can't imagine a person with no food wanting to drink alcohol. However, the liver may be in poor condition at the start, could be a problem.