That doesn't seem to be the case per NY Times

http://www.nytimes.com/1989/10/16/opinion/actually-prohibiti...

Citation needed. First that seems incredibly hard to measure. Second I doubt many people tried that hard to measure. And third, access to alcohol during prohibition was never reduced by much. It just created a bunch of gangsters and violence.

It is hard to measure, but yes, people did try, both at the time and in more recent eras. To some degree the end of the first World War was a confounding factor, but the bulk of the sources I've seen support the parent's claims. The real effect of Prohibition was to change the quality of the alcohol consumed, for the worse (and even more unfortunately, one of the darker episodes of Prohibition involved the US Government deliberately poisoning alcohol). So, a quick search pulled up this[0] as a reference, but I'm sure that you can follow your interests to other results as you deem meet.

[0] http://www.druglibrary.org/prohibitionresults1.htm