Somewhat related as I came to GE via NEXUS ...

At my NEXUS interview the CBP officer asked if I traveled under a different passport (since I was born outside the US). I told him that I did not and that the US was my only active passport. He advised that if I did acquire a second passport from another country, to come in and add it to my profile. He noted I could travel under both no problem but just need to register it as soon as it is issued. I would assume the same goes for GE.

In your case, I agree with what ESpen36 notes - official passports may not be eligible (I didn't see any documentation about those the last time I checked). I also agree that the time/place to ask is your interview. Bring the additional passport there.

As for the expedited line (at least for JFK), I don't recall seeing one there either. I could be wrong as I don't spend too much time in line!
I would assume you could just go to the head of the line or use the GE line and go directly to the CBP officer behind one of the kiosks. A good questions to ask the people in the red jackets at JFK.