Buying a car on SORN

Technically as long as it is insured a SORN'd vehicle can be driven to a pre-arranged MOT.
Driving it for a test drive if it is not insured by the registered keeper is again technically a no no unless your own insurance specifically states you are covered on a vehicle not owned by you and not insured by the registered keeper, check your small print.
The tax status takes a while to change. the last short term runabout I had was showing as taxed (by the last owner) for over a week after i had taken ownership.
If you buy it you are required to sign the V5C as the new keeper and you get the the new keeper supplement which will allow you to tax the car immediately subject to insurance cover and MOT obviously.
Essentially the new VED scheme means the government get extra money as you can get overlaps in payments as refunds are for whole months only and new tax starts from the first day of the month. So if you buy a car this weekend the previous keeper will get a refund on any tax from 1st May and the new keeper would pay tax from 1st April. George Osbourne then laughs maniacally at his cunning scheme to butt stuff the motorist yet again.........

All the above is guidance. I guess they could cross reference whether the date of new ownership matches tax changes but i doubt they are that organised.

I've done that - and it was exactly as jininwatford says - if you've taxed it using the buyer's slip then when the V5 it's all sorted. The records have it in your name and show it as taxed as such.