Yes you can. Whatever you as your leader end up with at the end of the day is the society you have developed, evolved, and led influence from.
This idea of a civilization growing and surviving and giving off a vibe of an overall culture mixture, rather than a branded national state, makes more sense to me.
Saying “my American civilization stood the test of time”…really doesn’t make as much sense.
It would make sense IF the available civilizations were not coupled with what happened IRL.
But if you play Rome, even if you are stable and well defended, you must follow the route of a Rome that was defeated.
If you are Maya or Aztec, even if you are undefeated, the biggest country in the map, with a massive tech lead... You are still en route to become a post conquest Mexico in the next era.
Especially the later man, how can I say my civ stood the test of time if I am forced to go through a demographic change that happened through the genocide of the people of my age 1 and 2 civs.