iPhone 4 as an iPod Touch?

I'm switching my family plan from T-Mobile to AT&T soon because I want to get a Lumia 900. My wife, however, is already using an unlocked GSM Galaxy Nexus that she wants to keep after the switch, so I was considering using her line's subsidy to get a $100 iPhone 4 to use without a SIM card, as if it were an iPod Touch, to get access to the App Store and play around with some apps and games. Will the iPhone 4 work without a SIM? Are there any problems I'm likely to run into trying to do this? Would I be better off selling the iPhone on eBay and buying a real iPod Touch instead? The last Apple product I owned was a 5th Gen iPod with Video so I'm a little behind on my Apple knowledge and I just want to make sure I'm not buying my way into a headache. Thanks!