Sailed on MSC Meraviglia 12/15 to 12/18. We stayed in a Yacht Club Deluxe Balcony Suite.
Yes, there was quite a delay for most passengers due to the ship arriving to port late because of a woman that went overboard on the previous cruise. However, we received a text from MSC informing us that embarkation would be delayed. We had a 12pm scheduled embarkation, and decided to arrive closer to 2pm.
Upon arrival, because we booked into the Yacht Club, the port staff took us straight in, through security, and into the lounge to wait to board. About 15 minutes later, at around 240pm, we were escorted onto the ship.