Speaking as a lawyer (well as a retired one) I find the “is it an Agreement or is it a Treaty” issue utterly fascinating. have been researching it to death the past few days (with some wonderful help from some Freepers) and I don’t think it is clear. It certainly hasn’t been litigated.
I’d sure love to see SCOTUS weigh in on this.
http://caselaw.findlaw.com/us-supreme-court/224/583.html
...Generally, a treaty is defined as ‘a compact made between two or more independent nations, with a view to the public welfare.’...
...We think that the purpose of Congress was manifestly to permit rights and obligations of that character to be passed upon in the Federal court of final resort, and that matters of such vital importance, arising out of opposing constructions of international compacts, sometimes involving the peace of nations, should be subject to direct and prompt review by the highest court of the nation...
...If not technically a treaty requiring ratification, nevertheless it was a compact authorized by the Congress of the United States, negotiated and proclaimed under the authority of its President. We think such a compact is a treaty under the circuit court of appeals act, and, where its construction is directly involved, as it is here, there is a right of review by direct appeal to this court...
Also:
http://constitution.findlaw.com/article2/annotation12.html#f405