Basically, yes. The hardware is exactly the same across all iPad Air/rMini models.
Not... quite. The problem remains that some carriers (the CDMA networks) have policies in place where they are either strongly reluctant (Verizon) or outright refusing (Sprint) to not activate an iPad if it's not one of "their" devices... that being, a device whose IMEI/MEID isn't already in a database that identifies their stock.
Even though the devices are completely identical, and perfectly capable of working fine on their networks. The reasons are purely bureaucratic, and purely turf-based.
So, if you think there could be ANY reason that you may EVER want to use your device on say, Sprint (though why anyone would do that, well, that's beyond me really), then you should get a Sprint model. Any other carrier? You should probably get a Verizon model.
Solely because the wireless carriers feel, for whatever silly reason, that even though there is no subsidy (and thus, no subsidy lock) for iPads, there should still be this impression out that certain iPads can only work on certain carriers.
I guess this is to try and prevent people from doing what most of us do: Buy an iPad with a "good but expensive" carrier's SIM pre-installed, then hang on to it in case we need it while trotting over to T-Mobile to get free data.
Why Apple plays along with this stupid game, I have no idea. But it's probably the worst-kept secret that the cellular hardware on all iPad Airs/rMinis are identical
It'll "just work." The Sprint LTE mini retina has the radio for AT&T's 3G/"4G" network too. And if AT&T rolls out LTE in your area, that'll work fine as well.
Well, Verizon might hem and haw at this, and try to say it can't be activated. You might have to persevere on this, but
technically, a "T-Mobile" iPad Air or rMini is perfect capable of using Verizon LTE and EVDO.