If any of the motors were mis-connected (reverse or wrong voltage), the individual motor's overload relay would trip pretty quickly (assuming they are installed and wired properly)
Running multiple motors in open loop v/f off 1 vfd is very common, but not as good as it was a few years back when motors had reasonable slip. Today's darn 'Design E' or whatever the feds shoved down our throat have 1% or less slip, so the torque sharing in multi-motor applications is not as good as with older 3% slip motors. You can soften the motors up a little with output reactors, but it still is not great.
Unfortunately, big money has already been spent on the system... I would have suggested either 1 vfd, or even better, a vfd for each motor, having 1 as a master and all the others as torque sharing slaves.