I have not done this but a friend was traveled with did. I think it really depends on the age of the children also. Her kids were 8 and 10 and she does not allow them to sign themselves out so she knew they would be in camp until she came to get them.
She had a bit of a reservation about leaving them but they did not do anything that would put them at any great risk and if something happened to one of them there was still the other. I would recommend a Carnival excursion if you do this so you know that you can't miss the ship.
They have some sort of emergency policy that they follow and from what I understand they can contact these tour groups at anytime so I would think if anything happened to them you would be able to reach you. Her kids had no problems and like she said, it is in the back of your mind a bit the whole time, but they are doing what they want and you get to do what you want.