Nope. One shuttle launch does more Ozone Layer damage than if you had dumped every R-12 air conditioner on the planet.
You are likely right. What do the ammonium perchlorate-laden Solid Rocket Booster weigh, each? And what comes out of them? Aluminum oxides, NOx's and chlorides.
Chlorine emissions from the Space Shuttle?
The main engines use Hydrogen and Oxygen. The SRBs burn a solid rocket propellant that is a mixture of powdered aluminum and ammonium perchlorate. The shuttle maneuvering engines use hydrazine with oxygen.
So where does the Chlorine come from?