In addition to ratifying the treaty, wouldn’t Congress have to authorize the funds? Or would the treaty itself be an implicit authorization?

FWIW, I predict: Obama goes to Copenhagen, somewhat less expansively this time, and patronizingly plays the hero he imagines himself to be. He promises the moon to the Copenhagen cabal, comes back to America, offers it to Congress, and epically fails again. Obama-and-Copenhagen jokes spread like wildfire, and The One is burned so seriously that analysts declare another Turning Point in his presidency.