I'd say that a CC# has little impact desirability which means it has little impact on value.
It makes a knife more desirable to some, especially on the secondary market for models where fakes are common, as it virtually guarantees that the knife is genuine. If the knife is ever stolen, it can also aid recovery by making the knife easier to positively identify.
It also guarantees that the knife is early production, which is a two edged sword. "First Run" carries a certain cachet of desirability, but also means all the bugs may not have been worked out. Some less scrupulous sellers make it sound as if the number indicates a "limited run".
A CC# makes a knife less desirable to those who see any markings on the blade aside from tang stamps as disfigurement and to those with a bit of paranoia about things that might be able to be traced back to them.
For the rest, it has no effect on desirability. That last group is probably the largest.