Providing everyone is honest, then yes
Technically though, a pedigree or a registration does nothing more than list whom the breeder
says are the parents of a puppy. And in turn, the dogs listed as their parents are those that their breeders
said were the parents. There are no checks and balances - it is purely an honour system (unless someone makes a complaint, of course - in which case, the AKC may verify the breeder's word via a DNA test. Which would tell only that the dogs named as the parents are or aren't - not whether they're purebred).
As you would probably have a good idea already in this world, some people are more honest than others. There are plenty of dogs walking around that look nothing like the breed they're supposed to be but have papers "proving" their purebred status

But there are plenty of honest and ethical breeders also.