That actually happened to a friend of ours on our cruise last week. When we were in Antigua he was in the casino, winning and drinking a little too much and lost track of time (our ship was Jewel of the Seas and the Norweigan Jewel was in port too), he asked someone in the casino what time the ship left and they sayd 6:00, but we were leaving at 5:00.
Anyway, as we were pulling out of port here he comes running down the pier waving his arms at us. But, because we weren't completely out of port he was able to pay someone who owned a smaller boat to bring him to the ship. The ship threw a life jacket to him, and put down a rope ladder, the guys on the smaller boat hoisted him up. And of course, he never lived it down from our group of 50 and the staff.
Someone with the ship said that if we were completely out of port he wouldn't have been able to get onto the ship, he would've had to fly to our next port.