Article 12
Consent to be bound by a treaty expressed by signature
1. The consent of a State to be bound by a treaty is expressed by the signature of its representative when:
(a) the treaty provides that signature shall have that effect;
(b) it is otherwise established that the negotiating States were agreed that signature should have that effect; or
(c) the intention of the State to give that effect to the signature appears from the full powers of its representative or was expressed during the negotiation.
2. For the purposes of paragraph 1:
(a) the initialling of a text constitutes a signature of the treaty when it is established that the negotiating States so agreed;
(b) the signature ad referendum of a treaty by a representative, if confirmed by his State, constitutes a full signature of the treaty.
I don’t read it that way at all, especially 2b. Thats why the Senate votes on these things.
Since the United States does not agree, then any signature would be invalid. The only way the US could agree would be for the Senate to ratify any given treaty.
IOW, a signature by Obama without the agreement of the US Senate would mean that "the state" had not agreed with the signature and the treaty would then not be binding.
There are a number of places in Article 12 in which the "state agree" language is used.