I gave this a try as the Inca, completed the ancient era and sucessfully entered the exploration one. Not much to say except that it does what it is supposed to do: You and also the AI stick with the initially picked civ. The specials of your civ appear when you expect them. The only - and purely cosmetic issue - I found so far is that the civ boni get listed three times (probably once for each age):
While that mod of course can't do miracles and fix everything one might dislike about Civ 7's approach to leaders and civs (e.g. you still end up with intial "non-sense" picks among the AI, though I noticed at least that the picks weren't completely random, but "related" choices were made) and the result might make certain civs stronger or weaker (as the given boni are just not balanced for having to float a civ the netire game, it is
immersionwise already pretty close to that the mod names indicates: A "classic" Civ experience.
In this light I would really echo the requests to allow also the modern civs for plaing from the ancient age one... Reason: I would like to play a full as e.g. Catherine with the fitting civ of Russia...also choosing a civ with late, 3rd age boni for yourself gives the AI picking a "true ancient one" a nice indirect bonus and makes the game harder
Do any of the exploration and modern Civs get their narrative events in antiquity?
I did receive the usual amount of events/quests, so I would say yes.
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EDIT: Now the first minor gameplay issue - if you start with a civ not supposed to be used in the ancient age, in the early exploration age you might lack policy cards to fill all spots:
Luckily this doesn't lock the game or something, you can just continue by leaving them open for the moment.