VFD - 12 Pulse Transformer - Wye Winding

The protection and SCR circuits for the delta windings are designed to work with an ungrounded system, there is no reason to ground the wye side.
If you ground it and the power converter was designed to be operated ungrounded, you could risk damage during a ground fault that the conversion equipment was not designed to withstand.

It’s also possible that it would make no difference, clamping unfaulted phase voltages to the L-N values, whereas on the delta windings you would design for the shift, and procure suitable components.

In conclusion, you would be best served by inquiring of the power conversion manufacturer as to their preferred source configuration.

Yes typically by grounding the wye secondary of a delta-wye transformer does help stabilize the line to neutral voltage which in my experience can also influence the circuit response and behavior in any circuit fault condition..

I'm not so sure that this applies to a 12-pulse system as well?

The earth ground in my view is typically used as a commonly used reference point for safety related applications in an electrical circuit, regardless of being isolated or not.