It shouldn't. You already have an iPhone and an existing contract with AT&T, right? As far as they are concerned, you are just getting a replacement iPhone (from Apple or from from other outside source). As long as you aren't changing your voice service, data plan, or anything else related to your monthly billing, AT&T shouldn't see this as an account change and renew your contract.
A few years ago mi wife moved her SIM card form her Blackberry Bold to my old iPhone 3G, and the onlything that AT&T did was to change her account so that the data service would work on the iPhone. No charges from them, and no contract changes, so that when her contract was up 2 months later we bought her an iPhone 4. When that iPhone 4 got dumped in water last month, we put her SIM card in my old iPhone 4 and AT&T didn't change her account and now that she contract is about up we are about ready to go get her a new iPhone 5... Funny how her phones seem to die right before her contract, and my old phones which have beeen out of contract about 6 months are still working fine to carry her over until she is eligible for an upgrade...
