This is a very interesting thought.
I would like to drag the Audrey around the living room and use it wherever I sit.
The wireless ethernet gadgets are kind of useless for Audrey if you still need a wire.
Yes a single ethernet connection does not use all the conductors in the cable. The only
caveate as mentioned is voltage drops across the cable. By using a higher voltage supply
and installing regulators local to Audrey, the intended effect can be acheived.
I believe that the LM2825 DC-DC converters with fixed output voltages of 3.3V and 5V would
provide the desired effect. These units require a DC supply of less than 40V. The supply
delivered over the ethernet cable should be as close to this as possible. Most power over
ethernet applications use 48V. Unfortunately, a 48VDC supply will not work for these converters
and is difficult to find in a convenient wall wart package. A 24VDC supply can be found
in a wall-wart package.
The LM2825s are nice and small and simple.
The only issue left is determining if the current requirements on these supplies is low enough
to utilize these 1A parts.