I've got no experience combining them, but I have the C&C core and Monsters and Treasure from years ago. They look compatible. Thinking out loud:
ACKS uses d8 hit dice for monsters (mostly, except a few 1d4 hit point creatures) and occasional pluses, where C&C uses a spread from d4 to d12 depending on size and toughness (but still commonly d8). Similar results in many but not all cases, really. I'd use C&C entries where available, but to convert an ACKS monster keep the number of hit dice and eyeball a die type based on size and any pluses (if you're even worried about that). Attacks and damage look close enough they shouldn't need altered. Convert AC and you're done.
C&C doesn't have a % in Lair number! That's a weird lack for a semi-clone of AD&D, but "Goblins, 2-12/40-400" show there's room for it. Just use ACKS % in Lair numbers when you need them.
Monster xp comes out pretty close. A little more generous in C&C (and a little more fiddly), but close.
Class xp requirements start the same for 2nd level (for the fighter, thief, mage and assassin, but not the cleric, but C&C clerics gets spellcasting at 1st) and stay similar up until name level where they start to climb higher in C&C (which has no hard level cap, so that's how they're putting the brakes on instead). Similar, but C&C's are a few points higher in the mid levels, but C&C's scheme for monster xp gives out a hair more, so back to rough parity.
I'm not going through treasure types line by line :), but keep in mind treasure xp equal to 4 times monster xp on average and you should be fine. Do use xp for gold, which is technically optional in C&C but holy carp would that be a slow grind without it.
Given both xp to level and xp from monsters are in the same range in both games, you should be able to use ACKS treasure assumptions and ACKS campaign chapter prices (ships, castles, domain income and expenses) as is, without trying to find a conversion rate.
I see that equipment chapter prices are different; C&C prices have a higher high end than ACKS for the best weapons and armor, and some classes start with more gold. If you want to be very thorough, you can re-price those to ACKS standards before the game starts. You're on your own there though, as I don't see an obvious conversion rate. I don't think anything breaks too badly if you don't (unless and until your players take up arms smuggling in the trading game), it just avoids a "gear shift" later on. In theory I would prefer ACKS prices across the board so everything hangs together, but practically, the higher the price the more important you use ACKS' numbers.
Scrolls and potions are cheaper in C&C, so you'll have to make a choice there. If you do switch, at least item creation pricing is off in Monsters and Treasure, not the Player's Handbook.
I've only read DaW, and haven't dug into it the way some have on this board, so I'd welcome input. My own impression is you could use it out of the box and be pretty close to the results of a mass battle in C&C 1-to-1 scale, probably closer than any other mass battle system I know. But if you get into building your own custom units you'd probably want to first convert C&C monsters to ACKS stats.
TL;DR - You should be able to use C&C rules on the player's side and ACKS campaign rules (strongholds, domains, hexcrawling encounter odds and % in lair, etc.) on the GM's side with no problem. Lairs and Encounters should be useful for you if you're planning any kind of a sandbox or hexcrawl game.