

The point of bringing up the treaty is just to point out that the result of the situation you are describing was so scary that for about 30 years the 2 biggest nuclear powers agreed not to do it. That is all to say that one answer to your question is " US and Russia pretty much saw your scenario resulting in inevitable full scale nuclear war"
This is a very interesting concept. They would have to be born in order to be a (natural born) citizen I think. But, it should still work because the census is required to count residents not citizens