In theory it will work. However, knowing the way these things are, it will likely be locked to the carrier you choose.
I think this is unprecedented and we're just going to have to try things out ourselves.
I also talked with an Apple Rep:
# You: So in theory, one month I could use Verizon where my home is, then visit my folks and use AT&T where Verizon is not available.
#
Apple Rep: Let me check on that for you.
#
Apple Rep: That should work, yes.
The problem is that using different sims and carriers requires an apn profile change. It's easy to do but when you ask an Apple Rep, or an AT&T Rep, or a Verizon Rep, they may not know about this and even if they did, they would likely not factor it when answering this question about switching plans unless you bring it up specifically.
If you do not know about apn profile switching on an iDevice, then most of this would seem impossible.
But here we have a real interesting case of a Verizon device with all the GSM bands and should be unlocked. I don't think there has been a single device like this before as I'm pretty sure every Verizon device before has been locked, with or without the bands.
I ran into a similar conundrum when the iPhone 4S came out as a "world phone," basically I ended up wanting to learn if the Verizon 4S could be used on either AT&T or T-Mobile since it had the bands:
# World phone
# UMTS/HSDPA/HSUPA (850, 900, 1900, 2100 MHz);
GSM/EDGE (850, 900, 1800, 1900 MHz)
# CDMA EV-DO Rev. A (800, 1900 MHz)4
I don't think any of the folks who wanted to find out themselves reported back, but I believe that Verizon locked the GSM side from being used in the US. But then, that was the iPhone 4S purchased on contract so it wasn't that much of a surprise.
The iPad is a different matter, since you buy it without contract and you are not obligated to have a data plan. The previous iPads were unlocked and so should this one be. So going from Verizon to GSM should not be a problem unless there is a lock or something else happening beyond logic.
As a side note, I was curious what all the options could be for data on the new iPad, and I have to say that AT&T and Verizon seem to be the best $/GB (both T-Mobile and Simple Mobile for instance were pretty bad). So at least for now, I would consider getting a Verizon iPad to have AT&T data options if that would work, but there is no reason to look beyond those two unless you have a grandfathered plan.
Thinking long-term, though, the AT&T has 700 and 2100 LTE, while the Verizon model only has 700. Is this significant down the road?