tdracer,
It depends on how hypothetical you want to get I suppose, but as nothing more than a straight answer to your question, notwithstanding the structural damage to the underside of the aircraft that would occur, yes you would be able to lower the undercarriage, but not via the normal system. For normal operation, the Vulcan was fitted with three engine driven hydraulic pumps, plus an electrical hydraulic pack, which operated the U/C system, the braking system, Nose Wheel Steering system, Bomb Doors and randomly enough the AAPP inlet scoop.
In the event of failure of the normal system and in line with most military aircraft, the U/C could be 'blown down' using high pressure nitrogen from stored bottles. This, in our hypothetical Thunderball situation, is how the U/C could be lowered as we dropped to the sea bed!
I'm still not sure how we would manage to swim from the cockpit, through the No2 fuel tanks and into the Bomb Bay though!!
Flipflopman