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There exists a very strong argument that no treaty can violate pre-existing constitutional provisions without being void.

As a thought experiment, if a treaty was approved by 2/3 of the Senate which proclaimed the Pope as being the supreme and absolute ruler of the US, would that treaty be valid? Could we impose constitutional amendments by conducting a treaty with Burundi?

No. The fact that it's ridiculous to even consider the above means that a treaty is subordinate to the Constitution, and merely exists at the same level as any other federal legislation, and its validity is subordinate to its constitutionality.

As a thought experiment, if a treaty was approved by 2/3 of the Senate which proclaimed the Pope as being the supreme and absolute ruler of the US, would that treaty be valid?

Let's try a different question that answers yours. If the United States surrendered in a wary concluded by treaty, would it be valid?

The legal answer is yes. Treaties obligate a nation; a nation has a constitution. That's why "two thirds of Senators present" is such a disastrous provision. The degree of obligation is what is at question. Hence this recount of Henry's language at the Virginia Ratifying convention:

The power of making treaties, by this Constitution, ill-guarded as it is, extended farther than it did in any country in the world. Treaties were to have more force here than in any part of Christendom; for he defied any gentleman to show any thing so extensive in any strong, energetic government in Europe. Treaties rest, says he, on the laws and usages of nations. To say that they are municipal is, to me, a doctrine totally novel. To make them paramount to the Constitution and laws of the states, is unprecedented. I would give them the same force and obligation they have in Great Britain, or any other country in Europe. Gentlemen are going on in a fatal career; but I hope they will stop before they concede this power unguarded and unaltered

The practical answer may vary in your area, depending upon who has both the ammunition, communications, AND food with which to sustain resistance (the part that patriots seem to forget).