It does definitely need an IVA, until that's done every MOT is a risk that it'll get the box ticked and pulled in. If you get lucky with the first MOT, I'd stick to that tester as long as you can.
The only grey area is if it was involved in an accident whether the insurance could end up being invalidated if facts come to light and how much that could cost you if the accident was sufficiently serious. That's the risk you would be taking, how you weigh that up is a personal decision. Low risk, but potentially unlimited consequence.
Personally I certainly wouldn't buy it if an IVA would be impossible to pass, and it might be if there isn't documentation to support where all the bits have come from and when, or if you didn't want the hassle and cost of getting it through.
A bit off-topic but, I'm actually surprised that insurance companies haven't started asking for evidence of correct registration for modified vehicles. My Mini is actually a Mini based kit car, correctly registered etc. When I bought and insured it and explained what it was I expected to be asked for the V5 or IVA if applicable, as it is the insurance company only have my word and the fact that it's passed an MOT as evidence of what they're insuring.