normally, but there can be problems
I had an older compaq that I reinstalled using a non-OEM disk, and the key on the sticker. You are correct in that you'll be prompted to make a call, but in this case I was told I was SOL.
I don't know if I got a trainee on the phone or what. I asked to speak to a supervisor and was told to stuff it, the fellow assumed I was attempting to pirate the software and that was that.
So there is a weak link in the theory behind putting a sticker on the box; the the phone bank minions...