Insanely Fun DIY Science Experiments at Home with Physics Girl

Sooo, kinda. Not because the density changes during melting (which it does) but because the surface tension holding the drop to the ice pulls down on the ice, which pulls down on your hand which is connected to your body and requires more normal force from the boat which means it must be lower in the water just for having that drop. As soon as the surface tension breaks, the drop is in free-fall and experiencing no force except wind resistance and critically, no upward force besides the nearly incalculably small gravitational force. This means the boat would rise up to compensate for the smaller normal force it has to provide to you. Again, when the drop hits the deck, the normal force this time is applied directly to the drop versus through you and the ice cube so yes, the boat would have to dip slightly.