Not necessarily, depends on what hens you mate him too. It is a bit tricky though, because if the same rooster were a hen its possible she wouldn't show any leakage. Males typically show a lot more leakage than females of the same breeding. Best you can do is mate him to hens that you don't think have the same fault and try to breed away from it.
The neck feathers on a rooster are really only there to show off to the females. The Rooster may pass that same coloration to its male offspring. It varies on breeds. I hatched my first two BCM roosters about a year or two ago, and they both came out with different saddle, neck, and tail feather colors while one resembled the father rooster.