Chaos cultists are a troop choice in the new Chaos Marine codex, so yeah you can do it, although you'd have to have a marine or a DP as your HQ and pretty much all of your other unit options would involve marines as well.
You can ally with daemons and have them in the same army legally now too. If you want your cultists to have leman russ tanks and stuff like that, you can also ally with IG. But you can't ally with IG and daemons at the same time. If you want to have a mix of heavy ordnance and daemons probably the best way is to have an IG army painted up as traitor guard and ally them with daemons, skipping the CSM book altogether.