No. The court held in Rogers v. Bellei that the latter's citizenship could be revoked as a result of his not having met certain conditions imposed upon him by Congress under Congress' Constitutional power to "establish an uniform Rule of Naturalization." In so holding, the court observed that "our [Constitutional] law in this area follows English concepts with an acceptance of the jus soli, that is, that the place of birth governs citizenship status except as modified by statute." It identified in the Fourteenth Amendment "an express constitutional definition of citizenship. But [this] was one restricted to the combination of three factors, each and all significant: birth in the United States, naturalization in the United States, and subjection to the jurisdiction of the United States. The definition obviously did not apply to any acquisition of citizenship by being born abroad of an American parent. That type, and any other not covered by the Fourteenth Amendment, was necessarily left to proper congressional action."
In other words, Rogers v. Bellei did not address this issue directly, but it certainly didn't help Cruz's case.
As for the rest of the original post being "nonsense," no, it very much isn't. Inasmuch as common law colors our interpretation of the Framers' language and intent -- and it is humorous to note here that Cruz falls generally on the anti-Cruz end of this consideration -- the answer is clear. Blackstone tells us:
"The common law indeed stood absolutely so; with only a very few exceptions: so that a particular act of parliament [i.e. statutory, not common, law] became necessary after the restoration, for the naturalization of children of his majesty's English subjects, born in foreign countries during the late troubles. And this maxim of the law proceeded upon a general principle, that every man owes natural allegiance where he is born, and cannot owe two such allegiances, or serve two masters, at once. Yet the children of the king's embassadors born abroad were always held to be natural subjects: for as the father, though in a foreign country, owes not even a local allegiance to the prince to whom he is sent; so, with regard to the son also, he was held (by a kind of postliminium) to be born under the king of England's allegiance." [So, per common law, Cruz would have been a natural-born citizen only if his father had been in Canada on diplomatic business as a representative of the United States government.]
Furthermore, the legislation adopted in order to provide that children born abroad to American citizens were to be considered as natural born citizens stands in evidence of the proposition that such children were, as with the Constitution's common-law ancestry, not natural born citizens under Article II, Section 1 of the Constitution. Otherwise Congress would not need to create the law. [And the law isn't around anymore: I believe it was Madison himself who struck those words from the language in 1795.]