Probably... But, you'll need to figure-out how the communication is working. RS-232 would probably be easier to "tap into" than the wireless or USB. Do you know if any special drivers were loaded for the USB connection? Making a similar special-driver for the Arduino would probably be impossible. 
Or, are you thinking about leaving a computer connected to communicate with the Energy Monitor, and then connecting the computer to the Arduino to control relays, etc.? That might be possibe too, but you'd have to get the data out of their application somehow...
There must be some sort of relay, or indicator light, or something "obvious" that "happens" when it switches between solar and power-company (if that's the kind of solar system we're talking about). It might be easier to tap-into that signal, even if you have to set-up a separate wireless system to communicate with the Arduino. If you can run a wire, it's getting even easier...