Actually, that's just what I'm hoping to do: build a sort of EMI-only
"microphone" to use as a computer stethoscope. I figure that a computer
technician, with this tool and some practice, could hear and immediately
recognize the EMI signature of a dying power supply or other bad
component

Unfortuantely, most of that EMI is switching noise, which means it's
mostly a matter of what the program loops and I/O ports are doing... and
that may differ because machines' speeds are different. (I take it
you've never tried to debug asynchronous code...)

Worth trying, but I think it's going to be a matter of learning what
*your* machine sounds like in proper operation, then noticing when it
changes, then allowing for the fact that any change in either software
or input data may produce changes in the sound.