Assuming the VFD has supplies enough current and the correct voltage and frequency, why not? The fact you have asked the question makes me wonder if you have mis-stated the conditions or you are laboring under some misunderstanding.
A motor with capacitor start has a speed switch to
control the start winding. If you want to use a VFD, you should use it at a speed higher than then
internal speed switch setting.
You should not have any ramp speed inside your VFD in order to be as fast as possible at higher speed than that speed switch.
You generally can not.
The starting capacitor is designed to work at supply frequency.
The capacitor will have to disconnect at near the full speed by the centrifugal switch,Below this the current inrush to the motor will be huge.
Any operation below supply frequency will not disconnect the capacitor and draw large currents.
Prolonged high current will heat up the capacitor and will blow it off and burn the windings which are rated for few seconds only.
Also the capacitor is necessary to produce a temporary rotating magnetic field to make the rotor move. The axis of the magnetic field will shift and the motor will not have enough torque to pull.
If there is a series resonance between the starting winding and the capacitor in any frequency below or above the supply frequency, then the current drawn by the motor will be very high so as to destroy it.
You can still test the motor and VSD if you have these to spare.
Regards,
Sekar
If you are using a three phase drive, it will see the two legs of the 230vac motor, detect the open leg on the third. The drive may fault due to that open leg.