Moderate to high levels of chlorine break down polyquat, but only turn it into shorter chain polymers that are still effective. That's what the chemist at Buckman Labs told me (they make virtually all the PolyQuat used in the U.S., sold under a variety of brand names). Their recommendation for using PolyQuat upon closing a pool for the winter is to first shock with chlorine and then when the chlorine drops to normal levels, then add the PolyQuat.
As duraleigh said, PolyQuat is more effective at preventing algae than battling an algae bloom and its an extra expense that is unnecessary if you maintain chlorine levels. So if you believe you won't be able to maintain chlorine levels in your pool consistently and you have a bigger wallet, then a weekly maintenance dose of PolyQuat is insurance. Most pool owners that use chlorine or the BBB method to save on cost only use PolyQuat on closing in the winter, if then. I don't use it at all anymore, but my pool does not freeze over in the winter so I just keep chlorine in it (which is easy when the water temps are cold -- the chlorine lasts a LONG time).
