Simply no. Not if anyone is honest.
The French had a phrase used for translating natural born subject, and Vattel did not use that phrase. Nor did he modify that phrase to make it apply to NBC. He simply did not use the phrase,. He was a lawyer, writing on international law, and he did not use the French term for NBS/NBC.
The English translations of Vattel available at the time the US Constitution was written used “Native” and “Indignes”, not NBC. The copy of Vattel George Washington borrowed used native and indigne, not NBC.
Further, they used the term NBC and the term NBS interchangeably, and it is hard to argue that people who use either NBC or NBS at random attach one meaning to NBS and another to NBC. That is just stupid.
And finally, the US Supreme Court has already discussed the issue, back in 1898.
It is over. The meaning of NBC is found in the definition of NBS as used by all the Founders their entire lives.
Vattel was a respected authority on international law - the “Law of Nations”. He was not, nor did he pretend to be, an expert on colonial law. He was used regularly for his knowledge of European law, but the only reference to Vattel in the discussions framing or adopting the US Constitution was one time referring to proportional representation by the states.
There is ZERO doubt that the meaning of NBC comes from the commonly accepted meaning of NBS. One can be ignorant, or stupid, and you are no longer ignorant on the subject. You may choose to be stupid, if you wish.
What a whopper! Not only did the Founding Fathers make use of it heavily (it was one of the two books George Washington never bothered to return to the library!), it was cited directly by name or quoted by the Founding fathers throughout their work. I do not know if it was only referenced once specifically within the confines of a constitutional meaning, but your attempt to de-emphasize the text is extremely dishonest.
Further, they used the term NBC and the term NBS interchangeably,
Which you do not actually bother to prove (you don't provide a single quote or source for anything you've said), but which in itself is entirely irrelevant anyway, since, from my same quote, for emphasis, "The Judge James Duane in his ruling described the importance of the new republic abiding by the Law of Nations, and explained that the standard for the court would be Vattel. He ruled that the Statues passed under the color of English Common Law, must be interpreted from the standpoint of its consistency with the law of nations"
It's also a stupid argument in and of itself, since obviously Vattel distinguishes between one who is, by nature, "of a country," and those who are merely naturalized. That can only refer to a natural born citizen, and is probably the reason why I cannot find a single translation of Vattel's work from any year that does not contain the phrase "natural born citizen," as that is the clear meaning of the text, though sadly I cannot find a translation from prior to 1790.
Another problem I forgot to mention by the way is that Blackstone’s commentary on English common law also defines natural born citizens as deriving— if not at times from both parents who are citizens— then from the father who is a citizen, though he removes the requirement of being born in the country.
I’ve not seen any definition from Blackstone that says differently, so, either way, in the case of Ted Cruz, he is not rescued here.