It would put me off.
KC registration does not mean you are breeding to showing standards.
It does mean that all the relevant health tests have been done (nothing to stop breeders doing more), that the bitch is between 2-6 years old and has had no more than four litters, and no more than 2 c-sections.
I agree that doesn't guarantee that they're a good breeder, but the absence of those standards doesn't exactly show any better and gives greater scope for worse.
Also, it removes all progeny from eligubikitynfir regustratiin, so even if you got wonderful healthy pups, they aren't going to help improve the breed as a whole because they are no longer part of those who are known/guaranteed to be that breed.
And yes, very unscrupulous people will go to considerable lengths to pass off non-pedigree pups as pedigree, usually because of the higher price.
I'd always rather stick with a breed enthusiast type breeder (who will be happy to chat at length about COI, screenings etc) or a very reputable commercial kennels (probably found by the breed club, so wouldn't include those producing non-registered puppies)
If you don't know that working line cockers can of course be KC registered, then are you new to thus?
Those buying working dogs I agree will care more about the working reputation of the line (even though that does of course not prevent KC regustratiin as well) and that's all word-of-mouth recommendation. If you're sure you will get enough enquiries from those who work dogs (maybe they've seen yours in action?) then yes that will of course be a good way ahead (and indeed the odd out-crossing for performance reasons might make sense too).
It might take a while to grow that kind of reputation though. But do your dogs already compete successfully? Or are known to the working community some other way?