FWIW - I used Global Entry for the first time for entry into ORD from AMS on Friday. I am a Nexus user who applied and got instant approval into Global Entry. It worked fine.

Since I had some time to kill I stopped by the CBP office and got the sticker that people have been talking about. I simply said "I need the Global Entry sticker" and they took my passport and got it for me...took about five minutes.
^

Now I only wish that the EU programs would be available to Global Entry participants at now extra charge...(Privium, etc.)