OK, lemme back up a little.
Monitors are powered, so amp is inside of them. No power amp is used in this situation.
Monitors themselves are shielded, so as not to emit signal, or allow interference in. The inputs to the amps inside the monitors allow balanced, 1/2" and RCA.
The line to the monitors will come directly from the line-out/monitor-out of the mixing board.
There is a fair amount of stuff that will be powered nearby. A computer, an LCD screen or two, a couple effects boxes, a 4 port headphone amplifier, and my big VOX amp, though that won't be on often, usually only when using it to record.
Also, some crappy powered speakers will be there as well, not shielded. Of course, there's plenty of electricity running through the walls as well.
I guess my question is whether the fact that one side is 1/4" (unbalanced) negates the effect of one side being balanced.