Transformer at VFD (AC Drive) Output

For test bench purposes then yes, no problem. For permanent installations you have to be concerned for the transformer design because of the potential for high losses and / or saturation. You can ask a transformer mfr to make a transformer for you to address those issues however if that is a concern for your test procedure, for example if you need to guarantee efficiency.

I dont believe the output of a AC Drive is pure sinusidal, not sure how that will behave on the transformer, if you have 690v available on your step up transformer, possibly that can be your input to your drive(depending on your drive), then use your drive to vary the output voltage depending on what you need or vary the voltage on the variac.I am no expert ,but on a test bench with all the necessary safety in place I see no harm.

Yes,

it can be connected, but you must remember that the output of a vsd (V/f ratio) is determined by the vsd and not adjustable. In order to keep the flux in a motor constant the vsd will adjust the output voltage in relation to the frequency output set point.

So to use it for the motor test bench at different voltages can't be done unless you require a different frequency at each voltage