I assume so the liquid moves around and gets cooled evenly. If you didn't move the drink, the outer layer of liquid would get cold, but the inside would take longer to get cold as well
Technically not by convection because that is the movement of fluid to transfer heat in and out of something, like air conditioning. The bath is not a moving fluid it is a simple constant temperature. The spinning moves the fluid inside the can so more of it touches the aluminum wall, which is being cooled by conduction with the ice bath.