It’s not a treaty at all if it’s rejected by the Senate. But President Obama can sign an Executive Order that orders the appropriate Executive Department or CZAR or Secretary of State, for example to do as they are ordered.
Obama has enormous power because he is the President. He does not have the power to sign a treaty with a foreign power without 51 Senators also signing it but he can sign a treaty that is rejected by the Senate or which is never presented to the Senate. That’s called an Unperfected Treaty and there are hundreds of them. Christian Wiktor wrote an entire book about them.
So Obama has three choices, two of which bypass the will of the American people if he signs a Treaty With Iran. Only one choice involves someone else approving it. The other two are dictatorial in nature.
Is Obama tyrannical enough to purposely sign a Treaty With Iran without consulting the Senate? Of course. Obama will prove to be the most dictatorial American President who has operated without the advice and consent of the Senate. It’s like being given permission to ignore a red light and driving while it’s red.
If Obama fails to present the Treaty being negotiated with Iran to the Senate he will show how disdainful of America and the Rule of Law he is. Prediction? He will not present his deal with Iran to the Senate. He doesn’t have the respect for Authority. He’s made that clear on many occasions. What a guy.