I guess that the only way find out whether an insurer will allow the no claims history accumulated on a Motability car can be applied to a private car at the same time is to phone a few of them and ask. As you say, NCD is based on the drivers history, so you’d think it would be possible, but answers may vary wildly by insurer.
When I joined Motability, I have kept ownership of a private car, which theoretically gave me 15 years good driver and many years NCB on my own car. If you remember, I also bought a Rover 75 V6 about 2 months ago, which technically meant, I would have to build up NCB from scratch on this car. I phoned LV, with who my BMW is insured with and asked if they would honour any no claims from either the good driver or my own built up NCB, without hesitation LV said we will ghost? you 5 year NCB on the Rover. I thought the price was high, so phoned Esure, which I have my home insurance with and again without hesitation (after a few questions), said they would honour 5yrs NCB, so the Rover is insured with them, as the price was better however, as of yesterday the Rover now resides with my dauhter as a named driver – dads are too kind 😂