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I certainly would not try this unless all the other circuitry on the secondary side is also referenced to PE. Basically that means I would only connect this capacitor to the local GND (which might also be PE). But even that is something I would be very cautious about.

Fundamental question when discussing EMI issues: What is the source of the noise, and what is the victim you're trying to protect?

There are sometimes valid reasons to add capacitance between "grounds," and this is based on identifying the source and victim in the system. In this case, I highly doubt your signal generator on the primary of the injection transformer is either a source or a victim of common mode noise. Thus I don't see any benefit to adding a Y capacitor.