Interesting question. If you are sailing, I would say NO, because if the boat capsizes, you do not want the child to be trapped under the boat by his tether line -- better for him to be thrown clear. (He is wearing a good life jacket, of course.)

If sails are down and there is no chance of capsize, and you are using an outboard motor, I would say it depends on how well the child obeys you as to where to sit on the boat. For a very young and active child, I would say you could use a tether from the center of the tramp that only allows him to roam to the edges and not enough to actually fall overboard -- same as what I would do with my dog in that situation.

If you put a long tether line, and the child falls overboard, even off the outside of the hull, there is a good chance that the line itself will get caught in the prop.