IF you have algae, the Polyquat is only partially effective against it, but chlorine is better. What you need to do is raise your FC to shock level and keep it there till the algae has been gone for at least 24 hours.

My preferred method of then adding the Polyquat, waiting for the FC to tumble, then raising it again, is based on the pool being algae-free FIRST.

I've never heard of the Polyquat filtering out that way, rather than you shouldn't backwash or vacuum to waste for about 48 hours at least. In my closing method above I always am running the filter. So I don't think your Polyquat is wasted.