I have had CBS with cleaners and have never had a problem. some people will tell you horrow stories about CBS but for me they have never been a problem and I wouldn't have a reef without one.
You can have them together, you just need to have a big enough tank where they will have their territory, I have kept cleaners and CBS together with no problems, but I do think you need a big enough tank where they will not fight.
I have both in my 180g and everything is fine. However, I also had them in my 35g hex before I transfered them. My mother has both in her 29g. So I think you'll be fine.