We've done it as well...on the 7-night western, we wanted to do the 4-elements with DD(10) while the ship was in Coz. The twins (DD(7) x 2) stayed in the kids club for the hours that we were gone. We alerted the club that we were going on the excursion, and the name and times of the excursion (the excursion was chartered through
DCL).
As far as what would happen if something went "wrong", well, there are a few times that we do similar actions...when the kids are in school and when they are being babysat are times that come to mind. Often, while the kids are in school, we can be an hour away, so if "something happens", we have to rely on child care professionals and friends to handle the situation until we get back.
The big difference with a cruise excursion is "getting left behind" if you get back late from an excursion...which is why in those cases we book through DCL, as they 'hold the boat' for you if your excursion (again, booked through them) is late...or at least that seems to have always been the case in action, if not in policy.
I've been wondering about the same thing. What happens if the child wants to leave the club and the parents are not on board the ship?
Our instructions to the twins...CHILL. We did things special for them, but we expected them to chill in the clubs while we did the special excursion with DD(10). In the end it was no problem, as they had friends in the clubs, and had a great time!