No - it sounds like the breeder here purchased their dog under limited registration. Breeders will register dogs with limited registration because they don't want people breeding unless the buyers are established in the breed or working with the original breeder on showing/health tests/etc. Likely too that the puppy wasn't up to standard in some way, so should not have been bred in the first place. So they register with limited registration so IF the buyer does breed, the puppies (your current dog) cannot be registered.
As a result, any offspring that comes from your dog will also not be able to be registered.
As a result, any offspring that comes from your dog will also not be able to be registered.