Most people walk around believing that the answer is Yes. How else does one explain the presumed connection between the people who now live in Greece and the Athens of Plato and Euripides day? Or the Egyptians of today and the Pharonic Era when the pyramids and the library of Alexandria were built?
There is no connection in any of these cases nor is there any connection to most other present day populations.
The Incas have remained a fairly separate population from the many new arrivals to the Americas, and the little intermarriage has resulted in very little cultural transmission.
In the case of the Greeks, we usually think of Greek civilization in connection with Athens which was defeated by Sparta. Greece was overrun by Macedonians then Romans and then Huns and a dozen other settling populations since then.
Pharonic Egypt was defeated, overrun and often settled by Hittites, Persians, Greeks, Romans and finally Arabs. It was the Greeks and the Persians in Egypt who created the library at Alexandria.
Don't look for democracy of the Athenian type in contemporary Greece or high civilization of any sort in contemporary Egypt. Nor should you ask me to read a quippa (set of Inca ropes) or lay stones in the Inca tradition. There is no historic connection in any of these cases.