The UN has no jurisdiction in State matters and the US should not be usurping State authority by signing treaties it can’t enforce.
And what will they “consular officials” do? They aren’t U.S. attorneys - my guess is they’d try somehow to have them brought to the consulate, at which point Jose is outside the back entrance with the motor running waiting to drive them home.
Maybe the “World Court” could make better use of their time trying those U.N. Peacekeepers for rape and molestation, since they seem to be so bored they need to interfere in our judicial proceedings.
I refer you to Article VI:
This Constitution, and the laws of the United States which shall be made in pursuance thereof; and all treaties made, or which shall be made, under the authority of the United States, shall be the supreme law of the land; and the judges in every state shall be bound thereby, anything in the Constitution or laws of any State to the contrary notwithstanding."
Any such treaties that assign a legal jurisdiction in the U.S. higher than the U.S. Supreme Court to any other entity (such as the U.N. and its constituent courts) are unconstitutional, plain and simple. Treaties that contradict the Constitution are not valid. In addition, as the "supreme law of the land," no legislation or legal decisions can violate the Constitution.
I also refer you to Article III, Section 2, which states:
Section 2. The judicial power shall extend to all cases, in law and equity, arising under this Constitution, the laws of the United States, and treaties made, or which shall be made, under their authority;--to all cases...between a state, or the citizens thereof, and foreign states, citizens or subjects.
The only judicial power applicable to the Mexican nationals in question, per the U.S. Constitution, is that of the U.S. So, maybe they should have access to Mexican consular officials, but, as they have been tried and convicted in proper accordance with U.S. law, the Mexicans can not use the U.N. to stay the executions without violating our sovereignty, since the U.N. courts have no jurisdiction over crimes committed within the U.S.
Of course, they will continue to whine about us supposedly violating their sovereignty.