Sorry about that - my brain went in a different direction!
There are a few theories with the IntelliChem and the pump, since some folks say the IntelliChem works better with a longer pump running time. The bottom line: run it as much or as little as you are comfortable with. You should not need to run it more than 8 hours a day (with at least 1 "turnover" of the water in your pool).
Personally, I would shut everything down just for the energy savings and, if you only have the cover off when you are using it or cleaning it, I would really recommend cutting down on the pump run time. Eight hours a day would be plenty. Your pool probably uses very little chlorine (it has a cover and is not subject to the sun's UV rays to eat it up). Your acid consumption would go down as well. Having said that, there is also a theory that constant operation with a cover causes the chloramine gasses to build up a bit and drive the OPR down - but that level of chemistry goes over my head.
If nothing else, less operation should equate to longer life for your equipment.