Potential noise source?

Is it possible that such a device could generate noise on AC lines

I have never read any complaints that it can/does. 

Like any electrical device you get what you pay for. There are cheap GFCI outlets with cheap contacts that don’t have good female to male plug blade contact pressure and better spec grade outlets with very good contact pressure. Better chance of micro arcing generated noise with a cheap outlet than from the internal electronics.

That circuit board is completely passive so I can't see why any noise will be generated. The only time a current flows through the pcb is when those coils sense a current imbalance (the ground fault) and then that starts the process of tripping the outlet -- the coil induces a current to that 8-pin chip which trips the SCR which pulls line voltage through a solenoid and pulls the contacts to interrupt the power.

I have Trifield meter, GFCI are one of the highest EMF emitting devices in home. Just did a reading this very minute, GFCI reading at least four times higher than any other AC outlet in house. Transformers in general emit extremely high EMF, in audio components they should be shielded. Hard drives another notorious emitter. 

Assuming one has dedicated lines for audio system GFCI should have virtually no impact on it.