It does, but wasn't used in the Flight 1549 scenario. Wouldn't have made a difference anyway because there were holes torn in the bottom of the A320 that were larger than the ports/valves closed by the button.
(source:wiki

)
EDIT: Figured I'd post the quote from Wiki that I summarized:
The Airbus A320 has a "ditching" button that closes valves and openings underneath the aircraft, including the outflow valve, the air inlet for the emergency RAT, the avionics inlet, the extract valve, and the flow control valve. It is meant to slow flooding in a water landing.
[34] The flight crew did not activate the "ditch switch" during the incident.
[35] Sullenberger later noted that it probably would not have been effective anyway, since the force of the water impact tore holes in the plane's
fuselage much larger than the openings sealed by the switch.
[22]