That'll make no difference if they're going to do him for not displaying valid tax anyway?
The problem is that rule was put in place before the database was instantly checkable, so the only way to prove your car had tax was by displaying the disk.
The rule really needs to be updated, that said I don't think I've ever heard of someone being fined for not displaying, it the car is indeed taxed.
If you're really worried just print out the confirmation email with reference number so you can show you have purchased a disk a couple of days previously, so it will be obvious to the police that you are genuinely waiting for it to be delivered.