No
Your judgement about the UN's flaws is justified. To say that the entire organization top to bottom does nothing good is wrong. To fear that "a world run by those currently calling the shots at the U.N." is a realistic possibility is exactly analogous to religious style irrationality.
It's a goddamn environmental treaty Tom, not the end of Western Civ. We have signed hundreds if not thousands of treaties with nations AND with through the UN. If it was causing a serious problem we would pull out.