You have to use the regular lanes at security, but you can use the Global Entry kiosks in immigration. You can get to the Global Entry kiosks without being in the NEXUS security lane. You don't need anything to "prove" your GE membership; just walk up and use the kiosk with your passport or green card.
That's what I thought - which sucks big time!
In that case the benefit of being a Global Entry member is much more limited, since the hold-up is generally at security.