The paddle will float for a few seconds. Most adjustable paddles do not float, as there are ways water can get in to the paddle at the attachment and adjustment points. While paddling, the best place to rest the paddle when not in use is on the board and securely placed under the bungee cord. You are also able to secure the paddle to your wrist using a leash.
On a side note, we would suggest rinsing and drying the paddle well after every session.