Is it possible to connect a phase control relay to an inverter (VFD)?
No, this is not recommended. The output of a VFD is not suitable of any electronics except the motor, you can't even measure it with your multimeter without putting it in a special low-z (low pass filter) mode.

The output looks like this:


If you'd want to do this, you'd need a harmonics filter in front of the three phase monitoring relay. And then there is no guarantee the device would survive the other features of the drive. (eg: braking and dc hold)

The best way to detect if a VFD is active is to use it's IO functionality.  Almost all VFD's will have a one or more relays, analog (0-10V/0-20mA) outputs or digital (24V) transistor outputs that are freely programmable in the software.