That's incorrect.. Maybe for base, but Luck definitely modifies your critical damage.
Stolen from a post just below this one:
* Luck increases your Critical damage and your chance to cause critical hits (380 Luck gives a 78% chance to critical). It also increases your damage slightly. 3 points in Luck = 1 point of damage. Without Luck you won't critical very often.
But that still doesn't specify being an actual increase of raw damage or an increased % to critical damage.
It does most definitely increase your critical damage though.
So my guess, to answer the OP, is that no one knows for sure. Maybe someone that's played the CN\KR w/e version could answer this for you though.