I have never shown my GE card. In fact, I've never carried it. It's only supposed to be for land crossings. Before the full-up facial recognition, you just used the passport.
Only once did I get something odd. I went through the facial recognition and it lit up green and I guess the guy couldn't find me on his mug shot screen as he asked if I was GE and where I did my interview. Finally, he took my passport and let me through.
All the other times, I've just been waved through (though I always stop to make my declarations).