I'll add a recent data point with Alaska, too.

When I booked a ticket via my kid's account instead of mine and forgot that my Global Entry number wasn't stored under that user ID's profile for me, I was able to add the number when I checked in for my AS flight at BOS airport, even after I'd done online check in at home.

I did carry my GE card to use as ID when I checked in, but I didn't ask if she needed to see the card in that rare case or if knowing the number would've been sufficient.