IPhone – If I have AT&T, will the iPhone 4S work in areas of CDMA coverage only

Yes, the two models are physically different. The radio is different.

As per Apple's website, the radio frequencies aren't the same. The verizon iPad supports Verizon LTE, and as per this post, AT&T 3G. However, the Verizon iPad does not support all LTE frequencies that the AT&T iPad does.

From Apple.com:

Wi-Fi + 4G for AT&T model: 4G LTE (700, 2100 MHz); UMTS/HSPA/HSPA+/DC-HSDPA (850, 900, 1900, 2100 MHz); GSM/EDGE (850, 900, 1800, 1900 MHz)

Wi-Fi + 4G for Verizon model: 4G LTE (700 MHz); CDMA EV-DO Rev. A (800, 1900 MHz); UMTS/HSPA/HSPA+/DC-HSDPA (850, 900, 1900, 2100 MHz); GSM/EDGE (850, 900, 1800, 1900 MHz)

Notice that there are some differences between the listed frequencies. They're nearly the same, but not quite.

Edit:

To confirm, the difference is a hardware difference, not a software imposed limitation on AT&T LTE. From the Macrumors article:

The Verizon iPad hardware supports only the 700 MHz band for LTE to match the carrier's technology, while the GSM version sold for use on AT&T's network supports both the 700 MHz and 2100 MHz bands as used by that carrier.

If you're looking to travel internationally, go with the AT&T iPad. (I got the Verizon iPad because I wanted the free hotspot feature, which AT&T does not offer for free at this time.)

Not likely unless Verizon agrees to release that phone for another carrier. Have a look at this guide on identifying iPhone models:

• Identifying iPhone models

The iPhone 4 you have is model A1349 (that should be printed on the back of the device), and if so, it is a pure CDMA phone so you cannot connect it to a GSM carrier due to differing radio technology.

Even if you were to jailbreak it or get Verizon to unlock it, it's only going to work with another CDMA carrier.

So in the USA - you need to find a carrier with coverage in CDMA EV-DO Rev. A (800, 1900 MHz) and that's primarily Sprint and Verizon. Since there is no SIM card in this device, you might not need to get it unlocked, but that will be a dialog between you and your potential carrier if they can provide coverage to it at the same time as Verizon may have it registered as "their locked device"

Due to bilateral roaming agreements - each CDMA tower in the US can and does serve multiple carrier devices - so it's likely that Verizon could prevent you from using your device on a competing carrier until you fulfilled your contract or convinced them to release that device's status in the common database for cell phones.

There are well over 50 regional and national carriers providing CDMA coverage according to this wikipedia article so you might have considerable options in some regions of the US.

_{Nore some of the information is old due to consolidation. Your main bets are C Spire, Sprint and Verizon.}