I'm curious. The typical narrative about Prohibition is that we should laugh at the folly of the nanny state but I recall reading at some point that alcohol abuse was a much worse problem back then than it is now, that we are judging things by our own contemporary experience, and wish to know how true that is.
Well, according to a Freakonomics podcast I listened to last night this is a very difficult question to answer because there are no reliable numbers on alcohol consumption during prohibition, due to the government pretending the number was zero.
The way your question is phrased works quite well however for what they did instead, which was use a proxy, the proxy being number of cases of cirrhosis. When they looked at these numbers they found that prohibition had a minor to moderate effect in decreasing cases of cirrhosis, approximately 10-25%.
Again, it should be noted that cirrhosis is obviously caused by alcohol abuse, so these numbers speak less to consumption and more to your specific question about alcohol as a problem.