it shouldnt affect your shift speed.

Was the battery disconnected?

That can cause a reset of any learned parameters, but still, the shift points shouldnt change.

If the pulley doesnt wobble side to side when you press on it with the belt off, its probably okay. Spin it and listen for bearing noise, if there is an excessive amount, it probably needs replacing.

Otherwise thats $20-40 you can keep in your pocket for a while.