I get your point but this is kind of compounding two things into one. IVA by its very title cannot be "Type approval", as you are not getting a "Type" approved but an individual vehicle approved. so it absolutely is NOT "aka Type Approval". Type approval allows a manufacturer to manufacture a load of vehicles of the same "type", IVA is for one offs.
It might, and probably would, come under the heading of a radically altered vehicle. see
https://www.gov.uk/vehicle-registration/radically-altered-vehicles
As for your statement that a large proportion of Rods and Customs aren't roadworthy or legal, I'd like to know where you get that from.
I haven't been in that world for quite a while now but when I was, the ones I met at shows etc, that we did jointly with my kit car club, they were all taxed, insured MOTed etc. After all, the plods just LOVE to crawl all over that sort of thing!