Can I use a twisted pair cable to send power to a device that uses a micro-USB jack?
In general, you can use 22 awg cable to carry a few (7) amps. With two conductors, you doible the area, halve the resistance, hence halve the voltage drop and any power loss. Essentially like a single 19 awg cable. For 5V 2 Amps over 20 feet (round trip), you don't have much to worry about.

Except building and electrical code.