The White Sox had a player like that in 1975: Jim Essian. He came to the Sox in May as the player-to-be-named-later in an off-season trade that sent Dick Allen to Atlanta. Allen refused to play for the Braves, and they traded him to the Philllies, who sent Essian to the Sox.
Essian spent nine weeks on the Sox major league roster and never played a single game before they finally sent him to the minors. Chuck Tanner just used him as a bullpen catcher and played with 24 men.