Its a manufacturer warranty through a company that creates the device. I cant imagine they'd reject service because you arent with AT&T (seeing as you're PAYG).
It's not a requirement they activate it after service or swapping it etc. I brought mine in with No O2 SIM inserted, and of course, the guy asked for the SIM on that occasion, but on an earlier occasion the replacement iPhone had no charge and with genius appointments being 10 minutes a slot, he handed over the phone and told me to charge and activate at home.
I don't have AT&T, and have had my 3G replaced twice while walking in to the Apple store with no SIM card in the phone. All the genius says it that if you need to activate it, buy a GoPhone starter kit from AT&T, and activate it here. Hope this helps. I, of course didn't use this method and unlocked and jailbroke my iPhone as soon as I got home instead.
For what it's worth, Apple's support website specifically recommends that you should always remove your SIM card from your iPhone before you bring it in for servicing. So it should be perfectly normal and expected that your iPhone would show the "No SIM" message when you give it to the store representative.