I am getting way out of my knowledgeable area here, but I won't let that stop me... [grin icon]
In order to kill off cysts, you need a concentration in contact with them for a specified period of time. The dynamic nature of the body makes this very challenging.
However, I am lead to believe that cysts are dormant and do not multiply. If this is correct, and if using the mouthwash results in killing off some of the free floating pathogens before they transform to the cyst form, over time there could be a gradual reduction in the amount of cysts.
Of course, non of this has been studied and once again there are a lot of "if's" involved.