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In many and I believe the majority of XLR cables the "ground wire" is the shield. But regardless of whether or not that is the case in a particular cable I would expect that any sonic effects the characteristics of the ground conductor may result in will depend on the internal grounding configuration and other aspects of the designs of the components that are being connected. Best design practices will result in no signal current flowing through the shield or other ground conductor, but my understanding is that is not the case with many designs.
For that and other reasons I would not expect the sonic effects, if any, of the shield or other ground conductor to have a great deal of predictability, or consistency from system to system. And I'm not sure that keeping its metallic composition the same as the composition of the two signal wires is likely to provide any particular advantage.