If the explosives do go off accidentally, there is little likelyhood of a fission reaction. If there is, it would be a low yield "fizzle". The implosion around the pit would have to be damn near perfectly symmetrical for the fission trigger to go off. More likely if the 400# of TNT went off, there would be a lot of decontamination work to be done (and pieces of any techs nearby).
Yuppers.
Give underwater robotics, and undersea exploration work a few more years, an dthis can be done remotely.
Cost goes down, time goes down. Risk is reduced.
(Anybody want to start an underwater robotics company, apply for guvment grants to recover A-bombs?)