Obviously having them in the military would give a huge boost to morale and boost recruitment, but it would equally take a massive hit to morale if word got out that someone like DiMaggio was killed. I'm thinking that as a result they were simply used as pieces of propaganda to the American public, far from the front lines? Or did Joe DiMaggio and other period baseball stars really "take a swing at Hitler" and just managed to survive the war?
Joe DiMaggio enlisted in the US Army on February 17th 1943. He scored high enough on his Army Standard Aptitude Test that he was assigned to the US Army Air Force. He was assigned to the 7th Air Force and was sent to Oahu Hawaii. DiMaggio did not take a swing at Hitler, he spent World War II playing center field for the 7th Air Force baseball team that routinely creamed the various Navy, Marine and Army baseball teams in the Pearl Harbor area. He spent 1945 doing the same thing on the island of Tinian. His 7th Air Force baseball team was almost as good as the Harlem Globetrotters were at basketball. They won 85 percent of the games they played. DiMaggio resented his time in the Army. The fact he was paid a paltry $21 a month was a major bone of contention. He said Army life was extremely boring. With the exception of a six night-time bombing raids, that stopped once the US captured the island of Iwo Jima, DiMaggio was no where near the combat zone. Joe DiMaggio did not fly any combat missions. He was part of the ground crew. he drove the trucks that delivered bombs to the crews that loaded the bombs into 7th Air Force Bomber Command planes.
Source: "Joe DiMaggio: A Hero's Life" by Richard Ben Cramer.