That cycle actually points to the environment needed for the chemical reaction to occur.
Chlorine is responsible for the destruction of the Ozone molecule, O3. This reaction occurs in stratospheric clouds which form at temperatures <= -80C. These conditions are found only in the Antarctic winter, thats why it is a cyclical event. So yes, if our atmosphere continues to warm eventually the stratosphere will not get down to -80C...don't get excited though, we'll have enough to worry about down here in the troposphere
For a detailed explanation of the
reaction