This sounds nice, but is 100% FALSE. Research international law and treaties. The executive branch can bind us to a treaty until it is voted on by the Senate. The power originates from back in the day when the Senate was not typically in session and it was not easy for everyone to just travel for a vote. So the power exist to temporarily bind the USA to a treaty UNTIL THE SENATE VOTE ON IT. No one really foresaw the situation of the Senate refusing to vote on one, it was always assumed that they would do their patriotic duty to their country and vote.
Go read what Jesse Helms did with several treaties Clinton signed. They never made it out of committee, never voted on by the Senate, never ratified, and not the law.
Bill Clinton signed the Convention On The Rights of a Child Treaty on Feb, 16, 1995. It never made it out of committee in the US Senate to be voted on. The Republicans controlled the Foreign Relations Committee and never had the full senate vote on it. It is not the law of the land. Why would this be any different?