Yes Arfur they can. It involves the technique known as mixed gas diving where Helium is mixed in with oxygen. It is very much an area for commercial divers. Any underwater work to be carried out for extended periods of time involves bell diving with a compressed air chamber situated on the deck of the dive vessel, referred to in those circles as the pot, for the divers to gradually decompress to atmospheric pressure.
You are quite correct about human dexterity. In the event AAIB require for the wreckage to be recovered with minimal damage, then human divers at this depth would provide for greater chance of success than ROV`s. They would be able to place pneumatic lift bags at pre determined positions to maintain structural integrity during the lift and possibly raise it sufficiently above the sea bed before installing the wreckage in a cradle to bring it to the surface. It is all a matter of cost/benefit for the decision as to which method to use. A decision that I would guess to be made by AAIB, only they are in a position to evaluate whether they need the aircraft as intact as possible or otherwise.