You have to dissociate nations and clubs compe ions.
It doesn't happen so often. In fact, the georgian example is very marginal.
Maybe some "small" nation, or bigger eventually, will occasionally do it with a guy who's playing for a long time in the local country and is considered by all as a local and have been "assimilated" as it, but otherwise nations play guys from their countries. That's what makes those meetings exiting. People, fans couldn't accept to see a team who doesn't really represent their country, their history or culture.
that's why I don't think the georgian example would work, at term. It's more of a publicity or a rich man folly.