It happens all the time in the farm league before little league when one team is down a bunch of players. Usually the coach will lend a player to go over and sit on the outfield but still bat with his own team.
It's also usually one of the players who doesn't get a lot of playing time, like the bottom of the roster.
So in this case, it could still be a significant upgrade to their QB situation if they get a random player. Heck, even a random fan from our side would probably do better.