Not unless it is made of stainless steel or has a steel core, then the steel could scratch the barrel. If it is brass or bronze and has a bronze center core then no, no way it is going to hurt the barrel.
However, I have been cleaning ARs and everything else for many, many years and have yet to see a reason for a chamber brush nor have I ever had a problem with anything chambering related to a dirty chamber. Clean it well and there is no need for one IMO. One thing I would not do though, and that is ever take a brush and chuck it in a power drill. I can see no reason on earth for getting that aggressive with any kind of brush if the rifle has seen any sort of routine maintenance.