Probably not, start and run cap motors do not control that well, even with a VFD, they tend to drop out of run at low speed and/or with load.
The it most likely a Triac controller intended for Universal type motors or small shaded pole motors (fans).
You can either swap the motor for a treadmill DC motor and control or purchase a 3ph motor with a VFD.
The Dermal (Dremel?) is a Universal motor.
M.