There isn't a strong summer league over there to rival MLB. They do have a winter league- I'm a big fan of the Licey Tigres, but that's another thread- and a lot of the Dominican players play over there during the winter. They also have a Dominican Summer League, but it's rookie ball, and is basically for evaluation purposes.
A better example would be Japan's Nippon Baseball League. They've actually gotten some American players to go over there and play, and have been doing so for years, but they've never been able to attract a major star to go over there in his prime. The closest that they could claim would be Bob Horner in 1987, but the main reason that happened was because of collusion. It's usually guys like Tuffy Rhodes who palyed very briefly in the Big Leagues, but was a AAAA player, or guys at the end of their careers like MSU's very own Bobby Thigpen. A few guys have gone over there and starred like Cecil Fielder and then come back to star in the Big Leagues, but not many.
I don't know very many Americans that would want to go over there, and they pay fairly competitively to MLB- you would get more playing in Japan than in AAA for sure.