As
lucky said, the rules state that you have a departing flight to be eligible. Having said that, the Red Carpet Club in Newark is on the gate side of security (although just barely

) and it never hurts to ask. I seem to recall arriving in Newark, needing to check my email and asking if I could run in for a little bit and being admitted. One thing to watch out for (especially on arrivals from California) is that the Newark club closes at 8pm.