Just because Woodrow Wilson did it doesn't mean it's legal. Did Obama get the consent of 2/3rds of the Senate? Did he get advice? I'm talking "Constitutionally". Not what's occurred in the past. "Well, this guy did it" is not an excuse in my book.
No, no, sir.
Even though Wilson signed the Treaty of Versailles, it meant nothing, because the U.S. Senate didn't ratify it.
I vaguely recall Nixon and Carter signed some, but they came to naught because the treaties were never brought to the U.S. Senate.
It's a symbolic act, nothing more. Pa Kettle from the White House, in signing something with the Russians, is merely
promising to
try to get the U.S. Senate to pass it at some future time.