My guess without knowing what type of motor you have on the fan is no it cannot be speed regulated.
You need to have a 3 phase motor to use the VFD. Therefore no start circuit in the motor just 3 windings one for each phase to create the "rotating" magnetic field. The VFD would create a variable frequency output to control they syncronous speed of the motor.
What about repowering it with a motor for a furnace blower? Many of those are multi speed.