When mine was written off for a rear wing, bumper and tailgate, it was Cat C and needed a VIC.
In the space of a week it had one MoT (with advisories), VIC, second MoT at a different testing station having completed the advisory work (needs to be advisory free for my council). My car has never changed hands, but reissued V5 has a note on it saying summat along lines of 'Category C, substantial damage/repair'.
Al, I would suggest getting yours through a VIC, just to be sure.
The only reason a seller of a Cat C/D vehicle that they have repaired won't present it for a VIC is because they know it will be flagged up for summat
Question is whether a VIC is covered by the same rules as an MoT with regard to tax/current MoT
Suspect that if DVLA won't issue a new V5 without a VIC, then you won't be able to buy tax either until it's done. So to/from prearranged 'test' only unless on a trailer
Worth a call or pop into your nearest VOSA test site just to clarify...