The A/C will use more energy trying to dehumidify as well as cool. It takes less energy to lower air temp than it does for an air conditioner to convert the humidity in the air to a liquid and drain off your evaporator coil and then to the outside. It sounds counter productive but I assure you its not. Dehumidifiers use a lot less energy than the A/C and is designed for one purpose and that is to remove moisture from the air. Running both will in the long run use less energy than if you would just let your A/C run 24/7 and you will be more comfortable in the process. I spent a lot of time in College doing the numbers on this.