Hi, Keeper,
I don't think you'll hurt the rifle as long as everything works. But remember pull-through cleaners pull - they don't push very well. So if they stick, you're stuck, without a way to back it out.
They are often touted as a compact, emergency cleaning kit for the field, but they can't be used to get mud or dirt out of a barrel. Carrying a jointed rod is better.
There was a thread on this site about a guy having to drive one out with a dowel rod.
My motto: Pull throughs are no darn good!
Jim