I have a Pfister gt529fls Lisa kitchen faucet filtration unit installed, will a watts 500800 push hot water through it all the time?

It will use the cold water line as a return line so it would be normal to have this happen when the pump is running. If you put the sensor valve in the kitchen that would be where you would have warm water in the cold side again while the unit is circulating. If the valve is in a different location then you should not have an issue with their being warm water in the cold side at the faucet.