Under no circumstance can a runner advance if the batter commits backswing interference.
But there is a VERY MAJOR rule difference between High School/NFHS rule code and the OBR and NCAA rule.
In OBR and NCAA, the runners are simply returned to their bases – no one is called out.
In High School baseball, THE BATTER IS OUT if he commits backswing interference (the NFHS rule book calls it “follow-through interference”). This is in addition to the penalty that all runners return. If the follow-through interference occurs on a third strike, the batter is already out, so the runner on which the play was being attempted would also be ruled out.
