Now to our question. Are US citizens bound by this treaty?

No, because the treaty would never go into effect. Both Congress and the President lack the power to enter into a treaty that violates the US Constitution, as your example clearly does. Entering into a treaty is subject to the same constitutional limitations as any other federal act - see SCOTUS’ decision in Reid v Covert.

But while an interesting question, it has nothing to do with the instant situation. The 1957 Convention on Refugees doesn’t violate the Constitution.

Wikipedia: Reid v. Covert - Wikipedia

When have we ever not promised to defend our borders and who exactly in the international community is going to have an issue with that?

We never promised not to defend our borders. We did, however, promise not to return refugees who face persecution back to their home countries. Which is why we can’t just expel asylum applicants without a hearing - because it would violate their human rights. And a lot of other countries would have a problem if we started violating international human rights laws and engaging in refoulement.