This is what follows from the GAE model as proposed in @Swamidass ’ book, even if the author avoids to formulate clear conclusions.
You yourself support my claim when you state:
Although a supporter of GAE, you “are not sure” that your suggestion (which is exactly what I myself suggest as well) is supported by GAE! A clear sign that GAE is at least ambiguous and can be interpreted as stating that:
Non-genealogical descendants of Adam do NOT share in the same “flawed nature” as those who descend genealogically from Adam.
I give a further argument:
Suppose a non-genealogical descendant of Adam gets married with someone who descends genealogically from Adam.
The question is: does the non-genealogical descendant share in the same “flawed nature” as the genealogical spouse?
If YES:
then there is no need of genealogical descent from Adam to be “Image of God and Fallen”, and you can dispose of the Figures 17.1 and 18.1 in the book, and reasoning relying on them.
If NO:
God makes it possible that someone sharing in a “sinless nature” unites “in one flesh” with a spouse sharing a “flawed nature”. Then, with much more reason would God make the offspring to share in a “sinless nature”. In other words, if marriage between people “without need of Redemption” and people “in need of Redemption” does not impair the work of Redemption, God would create human offspring in the same state of original grace Adam and Eve had before their transgression. And you can dispose of “transmission of the fallen condition”, and the GAE model becomes useless.
Once again: According to Christian faith after the first transgression all human persons come into existence “in need of Redemption”.
This said, GAE has the merit of prompting us to discuss in depth all these possible scenarios to better understand the reason why “the state of need of Redemption” (“the sinful condition derived from Adam’s fall”) becomes transmitted.