There's two distinct sides to this issue. Having them on will lower the evap rate and you will be able to keep "jumpers". But, the flip side is they will also hold heat in and based on what you are describing, make a chiller a neccessity. I cool my tank soley with evaporation using fans and cool incoming air. That allows my tank to have a larger than usual temp. swing which although is more like a wild reef, it can be nerve racking if I get a heat wave like this past Summer.
I personally prefer uncovered tanks because I don't want to block light and I want to allow maximum gas exchange. Tough decision though, as it is not in the cards for me to keep any kind of fish that jump.