I live an hour away from New Orleans. I always leave about 8:30 am and by the time I get through traffic and get parked I am usually in the terminal about 10:30am. There are porters there to take your luggage at this time and usually around 11am they start the checking in process. As far as boarding, I have boarded a ship out of New Orleans at 12:15 before. I am sure the Conquest takes longer for boarding but I've never taking that one so I don't know but my last one was on the Sensation and we was on by 12:30. Hope this helps.
Inspiration May 26, 2002
Holiday March 1, 2003 & August 21, 2003 & April 24, 2004
Sensation March 3, 2005
We got to the pier around 11:00 am, dropped of our luggage, parked the car, checked in and were having our embarkation photo taken by 12:05 pm. Our cabin was ready so we dropped off our carry on items. We went to get lunch, explore the ship and picked a great spot for departure. Have a great time.
This will vary greatly dependent on staffing for imigration/customs staff available for debarking. Also dependent on staff/debarking pax responding to imigration /customs/pursar bill calls pages promptly. Shipboard turn around time is usually great (1-3 hours from docking). Any./All wlll delay your embarcation. Cznnot be predicted in advance. Jerks be Jerks be Jerks.