The cover will prevent chlorine from gassing off as fast. It may also block some of the UV rays that break FC down. If you have an opaque cover, blue on top, black on bottom, it will block far more UV, but may not heat as well.

We had, as our first pool, an Intex Donut. I would keep an opaque solar cover on it, then use the Intex pool cover, which tied over the sides, when we weren't using it or rain was on the horizon. Between the total blocking of UV, the almost complete prevention of gassing off, and the virtual blocking of contaminants getting into the little donut, I would find chlorine levels would be stable for days at a time, even as long as a week. Going on vacation was a snap--shock the pool and cover it and two weeks later it was fine.