There definitely are some N express trains in Manhattan that aren't construction-related. I've been on them in the mornings during rush hour.
I'm not 100% sure, but I believe that when the Q is running to Queens (and stopping at 49th Street) they put some (definitely not all) N trains on the express tracks and terminate those trains at 57th Street. If you look at the N schedule, you'll see some Ns originate or terminate at 57th instead of Astoria. I think those are the express Ns.