As to the impact of foreign law, my own inclination is that it may have to be weighed to the second generation, in this following regard: How much does the foreign custom and law practically hold the descendant the specific person at question?
That is from a nation that maintains very close ties to its ex-citizens, and where the specific person, has publicly and repeatedly expressed a co-citizenship intent, I might not consider that person natural born, under the strong sense that the mention in the Presidential requirement clause should suggest. It is strong because it is a special, extra requirement and thus should be interpreted strongly and not weakly.
That is, there are cases that merit special consideration.
For example: what of the citizen who has always lived outside the country, but who was born to citizens who had traveled abroad? Such an expatriated citizenship can be passed down through many generations as best I understand. Maybe I am wrong.
I think in what the framer’s meant for the term there are clear lines of only a subset of NBC status — being born in nation of citizen parents being NBC, and being born out of the nation to non-citizen parents being non-NBC. But that in the middle — there is a determination to be made under some process (yet to be defined, there’s the rub) and that process would factor in cultural affinity and international legal entanglements both general and specific.
The Constitution does require that the President be "14 years a resident" of the US. It may be that such a person is a natural born citizen, but is still excluded from the presidency in the same way a person under 35 years of age is.
Some types can, but most cannot beyond the first generation. The very first immigration law, of 1790,
"Provided, that the right of citizenship shall not descend to persons whose fathers have never been resident in the United States:"