If you're trying to warm up the water, circulating during the day should help a tiny bit. Whether it's enough to notice is another question.
My reasoning goes like this. If you have solar panels, you should run water through them fast enough that the water coming out is only a degree or two higher than what's going in. That is, the heat transfer is most efficient when the temperature difference is greatest. If you have a solar cover, a lot of the heat transference is by conduction, same as in solar panels; therefore if the cover is on during the day, you also want to be circulating during the day, to improve the efficiency of that heat transfer. In my own covered pool, just the other day I measured 75F an inch or two down, and 65F elbow deep; this is with the pump off. So if I ran the pump during the day, I'd get a bit more efficient warming.
Without a cover, more of the heating is by radiation, so the benefit of mixing is less clear; although I hear the radiation effect is mostly in the top foot or two of the water, so circulating during the day should still help some.
Again, hard to know whether this has any practical benefit.
--paulr