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So, the president's signature alone may be enough for other countries to consider us a party to a treaty but the USSC would laugh you out of court if you tried to cite such a treaty to them as governing law, and rightfully so.
I'm sure many lawyers would laugh. Nevertheless, the Supreme Court considers Vienna settled law (it considered much of it settled before we even signed it), including parts that sovereigntist Republican administrations tried to express reservations to in the ratification documents. Surprise!!!