I'd say since they were both frequent All Stars and their careers overlapped for many years, there is a very good chance that it happened. But I'm sure that they met up in a number of exhibition games. Remember that both played in the same city - Boston - for a number of years until Spahn and the Braves moved to Milwaukee.
Williams was in Korea, serving as John Glenn’s wingman during the 1952 All-Star Game, but returned from war in time to throw out the first ball at the midsummer festival in ’53. Three years later, he hit his fourth and final All-Star homer, a shot off Warren Spahn in a 7-3 AL loss at Griffith Stadium in Washington. Williams was one of four players who homered in the game, a lofty group that included Willie Mays, Stan Musial, and Mantle.