No (if that is what broke off), it did so before the orbiter turned sideways, which makes sense.
We now know factually that the rear starboard yaw thrusters activated before the mystery piece broke off, and that there was some sort of problem with them as reported by Dittemore. That possibly could have turned the orbiter sideways.
What sort of force do you figure broke off the vertical stab if it wasn't caused by a yawing force?