It does save a little bit lah, but doubt it'll be something significant.

Conventional air conditioners operate at a fixed speed, delivering a fixed amount of cooling and heating. While trying to maintain a set temperature they operate on the 'stop and start' principle.
An inverter works like the accelerator of a car, gently increasing or decreasing power. It reaches the desired temperature quicker and maintains it without wild fluctuations.
Thus the power saving.