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Sure, but you're totally dependent on the honesty of the breeder. A breeder can enter any stud they like, it's almost impossible to police. I'm sure yours is legit, and you should be able to get a 5 gen pedigree through the Kennel Club (you probably have to pay).
I'm not trying to piss on anyone's chips here, it's just the current situation is crazy and lockdown demand is driving it. Pushing the price up is having serious welfare consequences.
I'm not sure being KC registered means lineage is trackable - plenty of breeders hang papers to up the price. But then I fucking hate the KC for all the unneccessary suffering that has been caused to countless dogs due to aesthetic breed standards.