If you just use the VFD as a 3 phase source, it can work. Usually is best when the VFD is much bigger than the load, and can stand the inrush as the motor starts. We have members who do that.
The contactor coils do not particularly like low frequencies if you do vary speed, though, they may chatter, drop out, and otherwise cause trouble with the controls. That's with AC coils, obviously, but also DC coils with rectifiers and filter caps. And, with a "matched-size" VFD, how do you start it?
You can start the VFD, and have it accel to a frequency and voltage that the contactor coils will accept, and then you can start the motor, but you are already at a point where the motor inrush exceeds the VFD capability, so it will not work after all.
If the VFD is large, sufficient to start the largest motor, with the others already running, then you have much better chances. That is essentially what the "Phase Perfect" is... It is a high current partial VFD, (just the 3rd wire) which is intended to operate any combo of motors etc up to its max HP rating. And with the Phase Perfect, you DO use the regular machine controls.
But, with a VFD employed that way, you need a large one. For a 1 HP motor, at least a 5HP VFD would be needed. And it is probably best to find one where the manual does not scream and squall about switches as much as the very paranoiac ones do. Maybe the authors of the paranoiac manuals know dirty secrets about their VFDs.
I would suggest some form of filter after a VFD that you want to use that way.... A load-side inductor, followed by a radio interference filter. Keeps down interference, and reduces other spike voltage issues as well.