I think it would also depend on the illness. On the last few trips we have taken at least one of our children gets sick at one time or another from too much excitement, food, etc. On our NC/ Florida trip last month DD#2 ate way too fast at dinner at her aunt's house and blew cheese cubes all over the 3rd tier at the Carolina Hurricanes game. She was fine as soon as she threw up. If I had a cruise to board the following day I would have done it, since I have seen this from my girls before and know it's not infectious.
BTW we are working on DD#2 to eat S-L-O-W-L-Y.
Robin M.