No but all dogs that are sold as pedigrees are not, so the only way to make sure that they are is if the breeder you get a dog from has registered the litter with the KC.

As for your own dog if it is not KC registered the only way you could now do so would be to get in touch with the breeder and ask them . Sometimes you can find out who the dogs sire ( Dad ) is and who its Dam ( mum ) is and if they are also KC reg you might be able to get your own registered.

It is not neccessary to KC reg but IMO it is better that a pedigree dog is so as then you can trace its parentage , health checks etc to see that your dog is from good lines .