Yes. A civilization is not a race. It is something above biology. The fact that nobody running things is related to the founder of a civilization does not mean that civilization has somehow fallen and been replaced anew. It means that, at most, a particular regime has fallen from power. Civilizations are larger than their leadership, even their founders.
Would anything really change if one day we realized that nobody in the US congress was a blood relation of the founding fathers? I doubt anyone would see that as anything other than an interesting blip in a new cycle.
As an example, the current state of Egypt is not the heir to (or continuation of) the Egypt of the pharaohs. Instead they are the heirs to their conquerors, descended from Arab armies that conquered Hellenistic Egypt (which itself already had a dubious claim to any links with the original, pre-Greek invasion pharaohs). They speak a different language, pray to different gods, and have an altogether different culture; they just happen to live where the pharaohs once had their kingdoms.
The claim that the Egypt under the Pharaohs of the 31st Dynasty had a “dubious claim to any link with the pharaohs” has some obvious logical difficulties.
Yes, because being Roman had nothing to do with ethnicity. Even people from Italy were not Romans at first. The Latins people allies of Romans(socii) fought wars to be recognized as fully Romans and only after winning some battles they got it.
In Jesus time only 10% of the population had Roman citizenship, like St Paul, but after some centuries everyone had it.
Something similar happened in the US, black people were certainly not fully Americans or even people at first, they were slaves, let alone native Americans, devoid of any right.
The survivors that were not exterminated(like native Americans) fought for their rights and eventually they got it, after having lots of their houses burned,their women raped and their men murdered. They were sent to World wars in the worst conditions at the most risky positions.
Rome was a way of living, way beyond ethnicity. You only understand it when you travel to places without this heritage, like China or Afghanistan.
When I traveled to China I was surprised to live in a place with no rule of law for example. The Rule is whatever the CCP leaders want today. I took so many things from the West for granted.
If you're talking about ancestry, most Turks in Turkey are descended from Anatolian and Balkans populations so...