Using twisted pair for supply
A possible negative effect could be the resistance of the wire. That's not caused by the twisted pair, but rather the wire diameter. If they're really signal wires the diameter will be rather small, and have a non-negligible resistance. The resistance will cause a voltage drop, which may become noticeable at longer distances.  

If the wire is thick enough you won't have any negative effects, but no positive effects either. The power supply has a very low impedance, so it won't pick up from the signal, and at DC it won't inject any disturbances into the signal wires either.