That would be 67, and the answer is NO. It's been done without a quorum too.
All it takes is a signature and FedGov, Inc. will start finding a way to abide by its terms, ratification or no.
What treaty has been ratified with the Senate lacking a quorum?
You make a good point about the executive branch working to pass rules and regs with no regard to the ratification status of a signed treaty.