This is a question which has as many different answers as there were celebrities or athletes drafted. Some served in direct front line units, others served in training posts, or in units that benefited from their training or experience.
Some notable examples include Jimmy Stewart, who earned his pilot's licence and commercial rating a few years before war broke out. He was drafted, and initially rejected for being underweight for his height. Initially enlisted, he applied for a commission and flew in non-combat roles and did propaganda and recruiting work before arranging an assignment to a combat unit due to deploy to Europe. He eventually flew combat missions over France and Germany, and finished WW2 as a colonel in the USAAF, before becoming a reservist. His rank of colonel was made permanent in 1953, and was later promoted to brigadier general in 1959, remaining current as a intercontinental strategic bomber pilot in the B-36, B-47 and B-52 as an officer in the USAF Reserve. He even flew as an observer on an Arc Light bombing mission during the Vietnam War in 1966.
Frank Capra was another example from Hollywood who served, albeit in a non-combat role, having volunteered as a 44 year old after Pearl Harbor was bombed. Capra was commissioned as a major and did all his service in the US Army making films, perhaps most notably the series Why We Fight.
As to athletes, Jackie Robinson is one notable example - a semi-pro footballer before the war, he was drafted and assigned as an enlisted man to the armoured cavalry, before applying for a commission and assigned to the 761st Tank Battalion. He missed combat entirely, due to having been court martialed over a racial segregation incident stateside. He was acquitted and honourably discharged after the war, returning to his sporting career.
Others used loopholes in the draft regulations to avoid combat duties. Ted Williams was initially classed 1-A (available for unrestricted service) before an appeal reclassed him as 3-A (deferred for hardship to dependents), which was unpopular and caused him trouble with sponsors. There was later service with the USMC as a Naval Aviator, and also in the Korean War.
Borrowing an example from Australia's contributions, Keith Truscott was a promising cricketer and Australian rules footballer (he played in the 1939 and 1940 VFL Grand Finals) before joining the Royal Australian Air Force and training as a pilot, flying Spitfires in Britain racking up 20 confirmed and 5 unconfirmed kills over his career before being killed in a training accident in Australia in 1943.
As the brief examples listed show, there were different outcomes for different cases.