Yes, it did. Prohibition in the United States, and the concomitant rise in bootlegging, speakeasies, scofflaws, and moonshiners was reflected in a number of the stories published in the pulp magazines from 1920 to 1923. The media attention on gangland conflicts like the Beer Wars in Chicago, the trial of Al Capone, and the rise of prominent crimnals like Bonnie & Clyde helped spur the interest in "hardboiled" pulp fiction which appeared in pulps including Black Mask, True Detective, and Gangster Stories. The amount that Sam Spade drank would be a caution, but that was part of his appeal.
In speculative fiction, Prohibition was usually a background element rather than a subject matter; most editors were not keen to get political, but most of them also didn't seem to have any objection to writers including alcohol use in their stories. In Weird Tales for example, popular occult detective character Jules de Grandin was no teetotaler, and was a frequent imbiber. Science fiction pulps set in the far future often had little to do with Prohibition, but those set in or near the present day could still address the subject; H. P. Lovecraft famously wrote "Old Bugs" in 1919, as the Wartime Prohibition Act was to go into effect, as a way to poke fun at his friend Frank Belknap Long's determination to get drunk once and see what all the fuss was about before it was made illegal.
Prohibition, it must be remembered, affected the pulp authors themselves. Some of them, such as Lovecraft, were lifelong teetotals. Others like Robert E. Howard were not yet of legal age when Prohibition came into effect, although this didn't seriously stop their drinking, it did affect what they drank, which was often homebrew, fruit extracts, or tonics. I've got a fairly long article on Robert E. Howard's drinking habits in the Robert E. Howard Bar Guide. One particular incident that bears repeating:
I’ve but come from the last wine-shop open—Ishtar’s curse on these white-livered reformers who close the grog-houses! ‘Let men sleep rather than guzzle,’ they say—aye, so they can work and fight better for their masters! Soft-gutted eunuchs, I call them.
WHich you can clearly see as a shot against Prohibition, which would be repealed in December 1933.