According to Buckman Labs who make Polyquat, the higher levels of chlorine with higher levels of Polyquat have the Polyquat get broken up into smaller pieces, but they are still effective (eventually they break down further but that is much slower) so having chlorine with Polyquat still works. It's also possible that you had something else in your pool consuming chlorine -- not the Polyquat.
As for adding chlorine when the pool is covered, the main issue is that of circulation. If you had circulation, then adding chlorine is no problem, but without circulation it would be too strong in one area and not strong enough everywhere else. I wasn't clear if you are winterizing your pool lowering the water level, blowing out and sealing the lines, and turning off the pump or if you do not get hard freezes and were just reducing pump runtime. If the latter, you could certainly add chlorine over the winter. That's what I do and I lose only around 1ºF every 2 weeks when the water gets to 50ºF or so.