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human
[ATLA] Would Aang have been born if Avatar Roku lived longer?

I've always been under the impression that Aang was born the absolute second that Roku died based on that one episode where we see Roku's history. Using this logic I assume every new Avatar is born the moment the preceeding Avatar is killed or dies. 

So if Roku has not died on his island trying to stop the volcano and lived another few years would Aang have been born but without the Avatar spirit?

Alternatively if Roku died a few years earlier than the he did in some unrelated incident would another air baby be the Avatar or would the Avatar spirit wait it out until Aang was born?

Edit: Since its been coming up a lot, the only reason I assume Aang's mother was pregnant with him while Roku was alive and why Aang was born when Roku died is because the episode "The Avatar and the Fire Lord" presents the Hand-off from Roku to Aang to be synchronous. I don't know, that's why I'm asking lol.
gpt
I also had impression that Avatar spirit joins the baby that was born exactly at the moment of previous Avatar death, so probably if Roku didn't die for some time more, someone else would've ended up an Avatar, while Aang would be just a normal airbender.