Flew into ORD from LHR yesterday, with a scheduled landing of 3:10 or so, and reservations for our final GE interviews at 4 pm (I know, tight planning, but it was our best opportunity to be at a GE airport for the right length of time for quite a while). The plane was ~40 minutes late, so we booked it to passport control, only to find a long line for immigration. We explained the situation to the agent manning the military/diplomat/etc. line, and she let us get into that one (which was very, very nice of her), which meant only a 5 minute wait or so. We ended up making it to the interview by 4:10, and the agents couldn't have been nicer about it. Both my husband and myself were processed in an efficient and friendly manner, and we received our final confirmation email by 10 pm last night.
Whew! So, a bit of an adventure at the end, and I'm very much looking forward to being able to use GE for our future entries.