Not in the way you mean, from what I can tell. You define "natural" as "not requiring the intervention of man". How does that relate to determining natural-born citizen? Man has to define it otherwise your definition is so broad as to be useless. "Not requiring the intervention of man citizenship"?
You can blabber on all you want. You can claim that natural-born citizens are only people born in the country of citizen parents. But you cannot point to a clear, single, universally accepted definition of natural-born citizen that agrees with you. And since you can't then it is up to Congress to define it by determining, as part of their Constitutional power to set uniform rules of naturalization, who doesn't need to be naturalized. You don't want Congress to do that? Fine, then who defines it and where?
This is why I don't like talking to you. I have to explain things to you that are axiomatic to anyone with intelligence.
Let me make it simple for you. If you have to pass a law to make someone into a citizen, they are not a "natural" citizen. They are an artificial citizen created through the action of a man made law.
No "law" is required to make a natural citizen. They are inherently a citizen in the manner they are inherently human.
It is like the distinction between a blood-related child of a family, and an adopted child of a family; Another analogy which proved to be too complicated for you to grasp.
What is so funny is that you seemingly have no trouble understanding "natural law" when it comes to slavery, but are completely baffled by it when it comes to citizenship.