Running during day will just help circulate water --- keep it clean/filtered, even out the temperature, etc. Nice things. But it will come at a huge cost in your energy bill, that isn't worth it.
I am in Phoenix on time of use (APS) and my rates increase between 12:00pm and 7:00pm. After 7pm the rates are basically cheap/free, up until 12pm the next day. I have my filter programmed to start around 8pm and shut off at around 12pm -- with different cycles/times of pump speeds (variable speed). This works very well.
Doing above, my electric bill didn't increase after getting the pool. But if you try to run it during peak times, you'll notice it. I just checked my APS statement, the cost per kWh is:
Peak = $0.213 (12pm-7pm)
Off Peak = $0.076 (other time)