Any and all conductors carrying current have an electromagnetic field around them, unless fantastically well screened. So, there will inescapably be interference between interconnects, but exactly how much? Audible?
Personally, I have never been able to hear anything, but, never say never.
In my experience, earth loops producing 50Hz hum, which are all but impossible to trace but are eliminated by removing an earth somewhere, are the worst problem.