From a technical standpoint, probably. If you look at the
technical specifications for iPad Air, they don't list all the carrier models separately like they used to (sort of like they're doing for the iPhone 5s now).
However, the other issue to consider is whether the carrier can handle devices with unknown-to-it IMEIs.
This thread has some information about that (particularly from the third page on). One person had luck using the Verizon iPad Air on all networks tested except Sprint, which was not tested (I imagine going
to Sprint or Verizon is more difficult than going
away from them). Someone else got the T-Mobile iPad and tried to move it to Verizon, but Verizon wouldn't give them a SIM since Verizon didn't recognize the IMEI. Other posters seem to think that simply buying a nano SIM yourself would work (though it appears no one has tested that yet). Who knows what other combinations may be possible--it appears all should be technically possible, with it being just a matter of what the carriers actually
allow (officially or unofficially).