It may not matter a lot if it is used to vary speeds or not. Once you use a VFD, you have the same sort of "pulse width modulated" output whether you vary speed or not.
If the electrics cannot handle it, they probably will not like it at any speed.
Also, you will have to start and stop the motor via the VFD controls. The VFD cannot handle the starting surge unless the VFD is much larger in capability than the motor, usually rated at least for 5 x the motor current as continuous output. Otherwise it will "fault" on overcurrent, and just shut down.
Some VFDs can be set to not shut down, but to limit current and keep driving the load. That "may be" enough to get the motor and workpiece spinning without a stall. Lathes with a clutch are much better for that, as they start with minimal load.