If you can afford the investment for a good VFD, it is very convenient for driving a motor-compressor. With no VFD, the motor starts and moves immediately to full speed, filling the air reservoir to the pressure set up and then the compressor is bypassed or stopped. With a VFD, the motor is allowed to start at a slower pace and then running the compressor at a lower RPM, as it maintains a constant air pressure, with no spikes. This slower startup extends the lives of the motor, bearings, gears, belts, etc, and could result in improved overall efficiency.
To avoid risks of premature motor failure, verify that the original manufacturer considers it “VFD Duty Type”.