Using Anschutz rifles as an example, repeaters don't have a tight a chamber as a single shot match rifle. But a modest single shot like a Cooey is not going to be more accurate than a Cooey repeater because the chamber will likely be the same.
Shooting for accuracy using a single shot adapter is helpful for two reasons, as suggested above. First it avoids damaging the bullet on it's way to the chamber from the magazine. Second, it can promote greater concentration when loading is done singly because it encourages slower shooting than with a repeater.