I am a USA/Swiss/Canadian citizen, just did it last week, no problem.
I didn't mention my Swiss citizenship (they didn't event ask), but I did mention my Canadian citizenship, because it was at a Nexus office, which processes both, the Nexus and GE applications at once.
If you happen to live next to a Canadian border, or you can fly in, just apply for Nexus on the "GOES" system, which gives you both for $50.