Cruisedad, I'm sure it also depends on the number of passengers that are delayed too. If it is only one couple then that probably isn't enough. If 25 or thirty people are being waited on, they probably have a greater tolerance to wait. (cheaper to wait than have to get that many people to the next port)
On our second cruise, we were delayed. We landed in Miami about 4PM. There were two late planes worth of passengers (I'd say about 20 people). The CCL transportation crew met us at the gate (you could still do that then) and basically had us run to the baggage claim, told us to point our bags out and then we ran to the shuttle bus while someone else grabbed the bags.
We had a bus ride that resembled the movie "Speed" (I know I saw the driver run at least one red light and the bus came close to two wheeling it around a corner or two). We pulled up to the ship, they didn't check documents or anything. We were literally thrown through a doorway at dock level along with our bags and we went up to the purser's desk to check in. It was quite a trip. The mom in law was sitting there in the main lobby crying because she was certain we had missed the family cruise when they closed the doors and we had not arrived yet. It was an adventure, and yes the ship waited for us. BUT, it is not the start to a cruise that I would ever want to experience again.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013