Obviously, we have no real life example of this, so we can't conclusively say that it is possible. But we can see if there's any exclusion possible.
One thing that comes to mind is genetics. Since a child receives precisely half of each parent's genes, for a grandchild to be exactly the same as the grandmother (genetically speaking) you need insane luck.
Starting with Charlotte, that means Elizabeth is genetically (50% Charlotte + 50% Peter).
You would then expect that the child of Elizabeth is 50% Noah (let's ignore his parentage), and the law of averages suggests that the other 50% consists of 25% Charlotte and 25% Peter.
This leads to some interesting conclusions:
- The odds of Elizabeth supplying all of her mother's genes and none of her fathers are astronomically low, but non-zero.
- Noah should be supplying the exact genes that Charlotte didn't pass on the Elizabeth, since Elizabeth can't be the one passing those genes of (grandmother) Charlotte "back" to (baby) Charlotte.
Actually, the chances of this working out are slightly better than you think (still very low though) We haven't accounted for Peter.
Until now I assumed that Charlotte and Peter have separate genes, but if Charlotte is her own grandmother, then Charlotte statistically will have 25% of her grandfather's genes (or at least some amount). That means that Charlotte likely already contains some genes from Peter, because he is her grandfather.
You could argue that that makes Elizabeth more genetically equal to Peter than Charlotte. Peter is more involved in this lineage than the story gives him credit for.
This "Peter in Charlotte" point actually negates the first bullet point. It doesn't matter which specific genes Elizabeth passes on to her child. The only thing that matters is that Noah supplies the exact other half of (grandmother) Charlotte's genes to (baby) Charlotte, precisely the genes that grandmother Charlotte did not pass to Elizabeth.
To summarize, the odds of this randomly happening are low, but it is technically possible and therefore we cannot exclude its validity.
There's an interesting missed opportunity here. Noah is the child of Bartosz and Silja, and he was conceived in the "before 1920" timezone, where Franciska also ended up growing old. Remember that Franciska is Elizabeth's sister and Peter and Charlotte's daughter.
If Franciska had been the mother of Noah, then there could be a completely reasonable argument that Noah carries a lot of Peter/Charlotte's genes, which would further improve the chances of this genetical game of "pass the buck" to work itself out.
But that is not the case, so it's not applicable here.