Sometime between half a billion and a billion years, the Sun is going to get hot enough that the Earth’s seas will boil. If nothing is done about that (for example, moving the Earth away from the Sun), this loss of carbon dioxide will be irrelevant. But unless there’s some war or other severe ecological catastrophe that wipes out 99% of all life on Earth, I expect there’ll be some intelligent life here indefinitely. And yes I expect somewhere along the way, some civilization will do the move-away-from-the-Sun thing.
Note it doesn’t really take a very advanced tech to release CO[sub]2[/sub] from rocks. Somewhere I read that they used lime at Çatalhöyük, which was 8 or 9,000 years ago. That could be wrong, but lime production was one of the first industrial processes.
Such evolutionary pressure is no guarantee it’ll take place. Breaking down carbonate rocks biologically to get its carbon will probably take a whole new suite of enzymes and other specific chemicals not currently in any life form. There’s probably no evolutionary path that life can take to get there. One could probably be gengineered, but that would require better gene tech than we currently have.