I certainly verify this statement as I have noticed it personally. When I had my old split air-conditioning unit, my average monthly bill was about THB 4,000. This was recorded as an average for a period of 2 years.
Once I replaced it with a new "Carrier" that is even bigger in capacity and fitted with inverter, I was shocked to see my monthly bill hardly goes over THB 2,000. It has been almost a year since I replaced it.
Definitely worth it. By the way, I live in Bangkok, just in case.