The danger with the floater is large concentrations of high chlorine/low pH "pockets" around the floater that will not circulate unless the pump is on. So... it would be better to have the pump running while the floater is in the pool, but if the pump is off, make sure and stir the water up really well before swimmers get in so that those "pockets" are dissipated. Also, if the floater floats over next to your liner and stays there for any length of time, it will fade your liner in those spots. Might want to consider tethering your floater from both sides of the pool so that it will stay in the middle, and remove it when there are swimmers in the water.

Janet