I have done this exact same thing, i.e., arrive on #2 and depart on #20; it was a couple of years ago. At that time Amtrak ticketed passengers could remain in the station overnight. However, the station closed at 10 pm and those remaining in the station could not leave for any reason until 5:45 am. when the station reopened. Actually we only had access to part of the station, the Amtrak part. There was a rent-a-cop, not NOLA PD, who was very officious but that part is probably variable. So, no food available, no smoking and uncomfortable seating. Also no access to the Magnolia Room. IIRC you could get Greyhound wifi if you stood as close as you could to the line that marked their part of the station. There were maybe 8 or 6 of us that night.