In line level equipment the presence of low noise levels is obviously less of a factor. It is known that every power supply creates some reactive current potential. The more equipment involved, the more of these reactive currents are present. And so it follows, the more channels that are mixed, the more background noise will be present. This occurs in the summing amps in a console.
Some equipment is more sensitive to noise than others so problems are often hard to predict.
As a rule though, high gain and high impedance equipment is where most noise is introduced because here is the most gain. The answer is no. The standard practice of lifting the shields at the inputs of power amps suits this application very well. Power amplifiers may run on unbalanced AC with little effect on hum. Balanced power can still be used effectively to rid a system of hums, buzzes and other more subtle artifacts in the most sensitive equipment.