If I wanted to put say a circuit for any type of distortion inside of a guitar, could I set it up so it can run on both a battery or phantom power?
Phantom power is a means of distributing a DC current through audio cables to provide power for microphones and other equipment. It's usually in balanced cable and direct boxes can give the option for it too.
A lot of industrial processing equipment use 4 - 20 mA sensing circuits where the output is modulated on the power leads as a current. Instead of a voltage output, you have a current output which is converted to voltage very simply with a resistor. Since this voltage modulates the supply voltage, the circuit must be designed to work over a range of input voltages. With battery operation, the output would still be a current.
Yes. Other people do it and sell it. Requires a TRS jack in the guitar and a phantom supply box with some short protection for when the cable is being plugged and unplugged. The positive of the phantom on the ring, negative on the sleeve.
If you mean being able to switch back and forth, you'll need a shorted battery clip to replace the battery, or put in an spdt.