In theory, maybe. In practice tell that to all the kids who will soon be the majority of under-18 US citizens in the US...whose parents or grandparents came here illegally.
Reason I posted this is because AZ is considering a law that will declare "anchor babies" not to be U.S. citizens. If they pass it, it will certainly be challenged in court on the basis of the 14th Amendment.
If the federal government declares the citizenship of the children of the Russian agents null and void [due to the parents' lack of registration and, thus, lack of jurisdiction] - then AZ could challenge the court case on the basis that illegal alien parents are not properly registered either.