Some agents can change a reservation to add the wizard number without affecting the rate, and some can't.

Innumerable times I've had my wizard number added without a problem. But, I've encountered some agents who tell me the above story....that adding the wizard number causes the associated AWD to overwrite the rate (and AWD) in the reservation. I don't know why they can't do it, but the website itself has a screen asking you if you want to use the entered AWD instead of the associated AWD.

I've rarely had the rate change upon checkin, but the few times it happened I had to go to the counter with my printed reservation to get a manual adjustment.