Not sure if the calcium would dissolve very readily from the eggshell just floating in the water?
I did have a broken egg, empty inside, small hole on the top side, just smaller than a chicken egg floating in my pond yesterday. I'm hoping it is a left over snapping turtle egg and not the result of a raccoon raiding our mallard nest on the edge of the pond. I should have left the egg shell float in the pond and see how long it takes to fall apart?