They do consume a small amount of chlorine. But it should not be significant. The systems used in residential pools are so small they are of no real value. Removing it completely and not using any more electricity for it is the best move.I just started reading about ozone systems. Should it turn mine off? Not even sure how to do that.
It may set you back a day or two.
If just cloudy and no visible algae, a few days. If algae and green, a week or two. What filter type do you have? Your signature just says Pentair Filter.
Check all hiding places. If you are seeing dead algae then you still have live algae.
Cartridge filter will clear pretty well. Be sure to clean when you get a 25% rise in filter pressure over clean pressure.