No, we aren't. Anyone who thinks the U.S. is really subject to these international trade organizations should take a look at the ongoing softwood lumber dispute between the U.S. and Canada. Canada has won this dispute on multiple occasions before every trade board -- including NAFTA and GATT -- and yet the U.S. tariff on Canadian lumber remains in place (going on five years now) and there isn't a damn thing anyone is going to do about it.
If the U.S. wants to ignore an international trade board, it will.
Don't eat Canadian Beef. Got bugs in it because Canadians feed them guts.