Anything is possible. BUT you'd have to constantly charge the battery, which wastes energy, and using that inverter wastes energy, and all said and done, you've waste a lot of energy converting 120?AC to 12?DC then 12?DC back to 120?AC. Short answer though is yes you CAN do it, but your going to waste a lot of energy in the process.
Why would you want to do this anyway?
Two very important things, first batteries are EXPENSIVE (a good deep cycle battery is $100+ a piece) and your going to need quite a few to do what your thinking about. Second, why can't you use more than 600W where your at now?1.) can't use more than 600 watts at current place.
don't mind spending extra money if that means i can use more juice and charge a battery at another location.