@Brandon ***********
It seems much more likely to me that it will be the other way around.
As a non-O visa holder with a yearly extension (and re-entry permit) I already have a valid permission-to-stay stamp in my passport. Adding another stamp on re-entry serves no purpose at all, and anyone (bank, hotel, police) looking at my passport can easily see at any time that I am legal. So using an e-gate for re-entry would be perfect for me, just like using the e-gate for departure was a month ago.
But if visa exempt travellers go through the e-gates on arrival and get no stamp, no one can tell from their passport whether they are legal or not. The only way to tell would be some sort of online check which is not always very practical.