Sounds like your leaving from NOLA.
We've taken two cruises on NCL from NOLA.
Our first cruise we arrived at the port approximately 0930. We spent the next hour in the line for security clearance. We boarded about 1115.
Our second cruise, we arrived at the port approximately 1100. The security line was non-existant, we boarded about 1115.
NOLA has a very small waiting area for those who've checkin in. Once the area is full, NOLA stops the security line. It doesn't matter whether your in Haven or not, there is only one security line. You cannot check in or visit the haven waiting area until after security.
we found there was little of no advantage to an early arrival. We now wait in our comforable hotel room until we can time our arrival at the port after the line has cleared, around 1100.