Insanely Fun DIY Science Experiments at Home with Physics Girl

My answer to the icecube in a boat. Shortly... Yes, but not noticeble.
Over explained...
The droplet gains momentum and when it hits the floor an impuls is givven to the boat. This force pushes momentairaly the boat down, but it is not a conserved force like boyency thereby the boat bounces back. 
However you will not notice this for the boyency is far greater than the impulse. The impulse is so small it could be seen as negletable.

Boyency is might be cool for your physics 101.