It might be possible to run a regular compressor through inverter circuitry, but I doubt it would be effective or as reliable as a compressor that is designed to run with a DC inverter.
The inverter varies the speed of the compressor. I'm not sure if a regular compressor can be run like this without damaging it. Internal lubrication might be an issue. Also inverter ACs use the newer and more energy efficient R410a refrigerant, while non-inverter models are on R22.
Comcept inverter is an experiment, it might not be as good as a real inverter AC but the real test would be to see if it makes any economic sense at the end of the day.