One of the motor experts like Jraef might be better to chime in here, but I would have thought that starting the DOL motor second would cause excessive mechanical stress, as there is no synchronization between the DOL and VSD motor. If the VSD motor is started second and is using catch on the fly, then the drive should detect the motor rotation and sychronize with the DOL motor, which will be rotating the VSD driven motor since they're connected to the same belt. I think this is what GaryS is getting at too?
I'm a pump and fans guy, but I am rather curious about this.
I'm not sure what applying voltage to the already rotating DOL motor will mean in terms of "starting" current. Is the start current lower because the initial torque to get the motor up to speed is reduced?
I remember that accidentally applying voltage to a high inertia centrifuge load that was still in spin down, made a rather nasty noise and its made me cautious ever since