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The AC safety-earth is just that, a safety measure.

The purpose of the third power wire (commonly called the 'ground') is to provide an independent path for fault current in order to trip the circuit breaker before the faulty equipment can kill someone.

The purpose of the earth attachment is to limit the power system potential rise in the event of a lightning strike. In most USA installations, the utility step-down transformer secondary center tap is attached to earth at the transformer, and each customer's entrance panel is also attached to earth. The earth is not a very good conductor, and there can be many ohms of resistance between these points. Lightning has sufficient force to overcome this setup if it strikes too close, but the arrangement does provide some protection against induced surges.

There is much confusion in audio because circuits contain zero reference points called 'grounds' and this sounds a lot like the term used in the power wiring nomenclature. The impedance between any point in a circuit and the zero reference point depends on the wavelength: for the audio band in domestic situations, all wires are "short" and can be considered as simple lumped elements of resistance, inductance, and capacitance. However, for higher frequencies, the distance becomes a factor and the wire must be treated as a transmission line.

Some audiophiles with technical training and who should know better have installed independent earth connections for the AC circuits feeding their equipment, and report improved performance. This leads to the idea that the quality of the earth connection is important for audio performance, and questions such as yours. An independent earth connection is a very bad idea for safety reasons, but I won't go into detail here.

The quality of the earth connection is important for the safety reasons listed above. It has an influence on the noise environment of the audio system, but not for the reason you stated. The noise environment includes the frequency ranges from audio through UHF and possibly beyond. The safety-earth wiring, no matter how well made, is far too long to be an effective 'ground' connection for much of this frequency range. Modifying the safety-earth wiring will change the noise environment, but not eliminate the basic problem.

Equipment that is double-insulated can avoid connection to the safety-earth power wire and any noise carried on that wire. This is the best solution that I can see. Unfortunately, much audio equipment requires connection to the safety-earth for safety. The noise that enters the system through these connections limits the ultimate performance. Audio systems contain their own noise sources, so this ultimate limit may not be relevant if the internal noise sources have not been addressed.

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