Gateway is on the 50 states, LOTS of people live outside. There are two ways to do it. You have a US permanent address, with a gateway. When you want to use Alternate Travel (instead of Gateway), they normally compare the price of your gateway travel to your intntl travel. If it's too high, they won't pay.
OR you have a permanent overseas address with a gateway of "XXX". Normally, the max price of a ticket they will pay for is about $450. I do a lot of overseas Alternate Travel, and it usually works. Some people jumpseat, to the US to start a trip. Others js to the US, and then the company buys them a ticket from the US, to where their trip starts. Some people use the zed fares to get to the US. Some of the time, I have asked to start overseas, so they often have changed my trip to start overseas, so then it is Deadhead travel, with a biz class ticket. The guys in the Phillipines were paying to fly to HKG, and the company was then either buying them a ticket to ANC, or DH them HKG-ANC. Most Asian pilots have an ANC base. Most Euro pilots have a JFK base. ORD also works well for overseas travel (like what I have).

My last overseas Alternate Travel: I ended in MEX. The company bought me a ticket MEX-ABQ, instead of flying me to my gateway. My last Alternate Travel overseas flight before MEX, I ended in MIA. The company bought me a ticket MIA-YYZ, for xmas. (Wife's family lived on the West side...Islington/Bloor area).

So, it is not as simple as having Gateway/Home Basing overseas, but it is doable, and many people live overseas. A lot also live overseas for Kalita.