Absolutely, and in some way's it started before national prohibition. Before the 18th Amendment, there were many counties that enacted local liquor laws banning the sale of alcohol. Many counties along the southern border banned alcohol well before the 18th Amendment. With much of the southern border being sparse in population, it led to a thriving trade of booze coming up from the south. The U.S.-Mexican Border Into the Twenty-first Century By Paul Ganster, David E. Lorey has a chapter of prohibition and the border. Think of like this, San Diego, El Paso both sit on the border with Tijuana and Juarez next door. US citizens could easy walk across the border for gambling and alcohol, both of which were outlawed a few miles to the north. This led a boom of border town businesses along the northern border of Mexico and also helped to pave the way for a pretty solid booze smuggling trade.

Keep in mind that, with the exception of Los Angeles (pop. 500,000), it was hundreds of miles from the Mexican border to any city where very much booze could be sold. The Southwest had no cities of any size before World War II. Highways were still primitive and cross-country trucking was in its infancy. Heavily laden trucks, or even autos, coming north from the border would have been quite conspicuous.