if the insurance company made an offer to the person that owned the car then DVLA will have the car on record as a cat D, or whatever cat it was recorded as, if the insurance didnt make an offer (usually by finding some small print in their T&C, which happened to me recently) then the car wont be recorded at DVLA. if DVLA dont have any record of the car and its damage and you have the V5 you can fix it up, insure it and away your go, but be warned, a cat D by law should be crushed, you can't even use parts off it, if you fix it up you'll be driving a death trap.
Happy motoring
Chilli