if you are shooting ACC they will bend but a carbon arrow NO
twisting a carbon arrow out of a target is not good because it can seperate the bonded fibers but just to pull the arrow strait out will not harm or bendthe arrow.

you can weaken a carbon arrow shooting at hard targets like foamlatex anamals a lot because there is no give and just downright hard on arrows
but just under normal shooting conditions and using a bag target will prolong the life of any arrow carbon or aluminum.