This statement is false in so many ways I am not going to bother with more elaboration beyond the link. The Federal government will begin alignment with a treaty upon the signature of any officer present at its negotiation pursuant to the Vienna Convention on the Law of Treaties, which the US never ratified. According to the Department of State, it is a matter of "customary international law." Read the link. I don't care what Reid v. Covert said.
Roger that. Even if the 2/3 never happens, as long as the agencies align themselves with the underlying meaning of the treaties, ratification by the senate is pretty much meaningless.