I don't know how many people died from not drinking but the people that continued to drink could have had significant problems. According to "The Poisoner Handbook" By Deborah Blum there were several poisonings that occurred with the bootleg alcohol that was consumed by people during prohibition. When alcohol for drinking is distilled the first part that comes off the distiller is methanol or wood alcohol. Exposure to Methanol can cause blinding and death if ingested. The problem is wood alcohol is more potent than ethanol (what is used to make liquor) and easier to make. So there were several poisonings associated with homemade liquor that would not have occurred if there were laws regulating the production of alcohol. Because toxicology and forensic pathology were in their infancy during the 1920s and 1930s in the United States there is no way to know exactly how many people died because of wood alcohol or drinking adulterated alcohol.

There was also a class disparity between these poisonings, richer people were able to afford higher quality liquor, which had less methanol in it. The poorer you were it was more likely that you would have easier access to low quality liquor which would have a substantial amount of methanol in it.

Today it is hard to find out how many people die from alcohol related deaths. Categorizing how someone dies is a difficult idea to get around. For example if someone dies of liver failure, that is likely going to go on their autopsy report but what caused the liver failure?

So the short answer is we have no idea how many people died from alcohol withdraw or from drinking adulterated alcohol.