Will this circuit work? Using USB extension on a potentiometer
Assuming you don't want a very accurate measurement (if so, you wouldn't use a breadboard), your proposal will work.
You may want to connect the braided shield of the cut USB extension cable (male part) to the GND only at the Arduino side to reduce noise.  

I wondered if plugging the male part of the extended cable into a computer or other USB device would hurt, but it will not: DATA+ is connected to A1 which is analog in.