Not really; they serve Hashut, father of darkness. Who is a Chaos god, but the whole reason he was imprisoned in the first place is that Khorne was not exactly his #1 fan. Essentially the traditional idea was that the CDs were mutated to some extent by chaos, they traded with the chaos hordes, but they were politically completely separate and would rather have cut off their own beards than actually be part of the whole "subject the world to marauding" thing.
Put it this way;
- The aim of the hordes is total chaos, under their four gods fighting amongst one another.
- The aim of the CDs is total evil order, with all other races their slaves, under their one god with the other chaos gods being put firmly in their place.
There's a big difference, and I think that should be culturally reflected.