We've used both the "VIP" lounge in the international departures area of GIG (you walk to the end of the hallway, by the small duty free shop, and go down the stairs; it's next to a TAM Gold Club, and is used by a number of airlines, including US Airways). Look for signs for a VIP club. We used it because we were flying Envoy Class on US Airways. If you're not flying biz class but have RCC membership, I don't know what the situation would be.
Not sure if you'll have time to get to the RCC club in GRU. Can take a bit of walking, depending where you're starting from, but if you just ask directions you'll get there. When we were flying Continental Biz-First Class to the U.S. out of GRU last year we weren't allowed to use the showers since we weren't United passengers (though did get the free snacks and booze). This past February when we asked about the showers (hoping the "merger" had changed things), we got a different answer: the showers were broken.
When taking domestic flights, you can't get to the RCC, etc., but there's always the American Express Centurion Club. Sort of a RCC-lite.