Cat C vehicles need a VIC test. Once done, the logbook WILL say something like:
1. Declared new at first registration
2. Substantially repaired and/or accident damaged; identity checked on {enter date}
My Sierra 2000e has this as it was Cat-C'd due to being hit in a rear door, which made it uneconomical to repair for the insurance company.
Category D vehicles do NOT need a VIC test. Any Category B vehicles WILL not be allowed back onto the road except in special circumstances.
Category A vehicles are crushers only.