Alas, no this is a myth and here's the scoop on the reality, with quotes from Montpelier.
Now here’s the truth: James Madison did not attempt to appoint a secretary of beer to his cabinet or endorse a manufacturing plant for the cause and solution to all of life’s problems.
According to staffers at Madison’s Montpelier estate in Orange, Virginia, the mix-up may have come from a letter written by a businessman named Joseph Coppinger. The December 16, 1810, dispatch hit up Madison for public funds to launch a national, but not government-run, brewery. Coppinger’s self-contradictory argument? To ward off “the baneful influence of ardent spirits on the health and Morals of our fellow Citizens” and improve the quality of existing malt liquors in the marketplace.
“The lack of an extant response from Madison suggests he was not amenable to this suggestion,” says assistant curator Tiffany Cole, on behalf of the research team at Montpelier. “Furthermore, the notion that Madison would support a cabinet post for beer production runs counter to his established views of limited government and executive powers.”