"If we observed some behavior in the world that we could not account for with our understanding of natural law, we would revise our understanding, and bring the new phenomenon into the fold [...]"

Well, of course. Tautologically, nothing can violate natural law, because that's what we mean when we say natural law. But, if Descartes were right, and there actually was a fundamental, causally potent mental substance that drove human action by exerting force on the physical brain, and all ordinary matter besides the mental substance obeyed the physics we know, then I should think it would make sense to use the term physics to refer only to the ordinary matter which obeyed conservation of energy and the like, and to have a separate term (psychology, I guess) to refer to the study of the behavior of the special mental substance.

I'm not claiming Cartesian dualism is, in our terminology, logically possible--that, I don't know. But it is, in our terminology, apparently conceivable to the extent that I can talk about it: maybe if I knew more, then I couldn't.