The change in chlorine of 2.2 ppm is 2.2 mg/liter or 1.2 moles per 10,000 gallons. The PolyQuat was 10 ounces (which I assume is fluid ounces liquid) which has 204 grams of PolyQuat which is 0.806 moles for one "poly" which has two nitrogen. Normally it takes at least 3 chlorine for 2 nitrogen to oxidize ammonia so this works out almost exactly correct in this case since (3/2)*0.806 = 1.21. In other words, it does appear that the chlorine indeed breaks down polyquat through breaking at the nitrogen and producing nitrogen gas (just as it does with ammonia). This would leave some other simpler organic compounds to oxidize, but these tend to be broken down much more slowly, possibly requiring sunlight and much more time. In other words, I would expect more chlorine to get used up, but over a longer period of time.
So unless your numbers were just a coincidence, it appears that PolyQuat is broken down by chlorine very much as if it were ammonia (since it is, in fact, an ammonium compound). To me, this means that using PolyQuat in the presence of chlorine doesn't make much sense. Perhaps in the presence of smaller amounts of chlorine the PolyQuat forms something akin to monochloramine and that this is what is effective against algae, but that eventually this breaks down more completely (rather quickly, it seems) just as a monochloramine would break down to nitrogen gas.
(I assumed that because PolyQuat is Poly{ oxyethylene (Dimethyliminio) Ethylene (Dimethyliminio) Ethylene Dichloride} that this is the following chemical formula:
http://www.chemblink.com/products/31512-74-0.htm
so molecular weight is 253.17 for each "poly" which has two nitrogen)
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