In the DS all inputs run in parallel all of the time.
That said the only inputs that ever draw any significant power are the USB and Bridge.
Both will draw less power when idle, but that depends on their inputs not on which input the DS is paying attention to.
The USB draws a constant amount of current + some current that depends on the sampling rate.
The Bridge is much more complicated in that there are many kinds of inputs possible with differing compute loads, think of it like a small PC.
On the other hand the DS’s power supply is really 4 separate regulators on two separate transformer windings, the bridge uses a separate regulator from the analog board…
I don’t know what you might think you can infer from all of this - it’s impractical to unplug the bridge when you select another input, unplugging the Ethernet connector will lessen noise going into the DS just a little bit, just as unplugging any other input will lessen noise a little.