I’d say that choosing a foreign-born person as your example is inaccurate because the US Constitution requires the President to be born on US soil. But seeing that the last time the Republicans put forward a foreign-born US national as a presidential contender, everyone glossed over the issue, and only ivory-tower types wondered about the Constitutional issue (e.g., who even has standing, as the concept is currently understood, to enforce the provision?) perhaps your hypothetical is right on point.