The compressor in particular will take some juice, unless it's a pancake style. A 2000/4000 peak inverter may even have trouble. Partly because of how many amps the battery and wiring can provide. A 700CCA battery is only providing 5000 watts at 7.2 volts, which is below the threshold where the inverter will shut down. A 2hp compressor will draw more than 5000 watts at startup. And the induction motor won't like a modified sine wave inverter very much. Circ, miter and jobsite table saws (all with universal motors) will do ok on that power though.