I think any alcohol dependence would be much more recent than that, I doubt asian glow (https://en.wikipedia.org/wiki/Alcohol_flush_reaction) would be a thing of we were getting drunk on the Savannah.
Source: http://www.independent.co.uk/environment/nature/chimpanzees-...
Here's also an extract from a BBC Nature documentary: https://www.youtube.com/watch?v=pSm7BcQHWXk
Apparently, the monkeys are divided among heavy drinkers, occasional drinkers or teetootalers in proportions that are roughly equal to those among human beings.
Also, many 'native' peoples in the Americas, Australia, and Oceania have large problems with alcohol abuse. Large areas of Queensland forbid any ethanol, even for medicinal use, because of these social problems.