Heh heh. I used to work with a guy who came from a country which doesn't (or didn't at the time, anyway) send a team to every sport in the winter Olympics. As a lark the office was pushing to get him into the games in one of the skiing events (he didn't ski).
Sadly, the country in question wanted to see some evidence he could ski well, since they didn't want to be embarrassed.
This already happens but for other reasons. Some athletes will move to a country that underperforms in the Olympics for their sport so they can qualify easier.