Twisting wires together certainly significantly reduces any outgoing noise. As the current flowing in each wire is equal and opposite, so will the magnetic/electrical field they generate be equal and opposite. Twisting the wires gets them as close as possible, so that most of the two fields generated cancel out, with minimal residual noise emanating from the pair. It's why heater wires in valve amps are twisted together. It may be a low voltage - typically 6.3v a.c. but it's a high current, and it's current that generates the noise fields. Without doing this, a lot of 50/60hz hum can be transmitted to the amp circuitry.