If they took the case and examined the theory that Vattel’s concept of what it is to be a “natural born citizen” would they not have to examine the framers’ intention in choosing the phrase?
I believe only two of the justices are strong "originalists", that is they believe that the Constitution should mostly be interpreted by what the framers meant when they wrote it. At least four are "living breathing" Constitutionalists, who think the Constitution needs to be continually reinterpreted by each generation. Some of the remaining ones fall in between, with one who leans towards "strict constructionist" - ie, the most obvious literal interpretation (which for Natural Born might be "citizen at birth")...
So, unfortunately, I don't think it's at all certain that even if they took the case that the Vattel definition would be the slam-dunk decider that many here on FR make it out to be.