iPad Air with foreign GSM carrier
Solution 1:
I won't be possible if your iPad is carrier locked.
If it isn't, it will work.
Solution 2:
No iPad has been carrier locked in the US so you are free to put whatever SIM you want in as you travel internationally without needing to hassle with an unlock.
Look at http://apple.com/ipad/LTE for details on what LTE bands are in use in various countries. You will note that the Air and Retina Mini have very generous channel coverage where older iPads didn't have mostly universal coverage and you had to pick and choose which channels your device would support.