Sure it would. He could draw 20 amps at 220 volts from 2 different legs of
110v 20a. The electrons could care less, and the rating of the wires is in amps. (Volts too for that matter but ordinary household romex is good to 600v IIRC.)Trouble would come in if he needed more than the 15 or 20 amps the wire could carry.
Of course this is just theoretical as the code does not permit this.