Do wires and electical boxes need to be protected on the un-finished side of basement?
No, but they do need to be secured to the framing according to the NEC schedule. You must staple (or otherwise restrain) within 12" of each box, and every four feet along framing members, centered on the board. By doing so you reduce the likelihood of cable damage due to snags and fastener penetration. 

A neat wiring job involves straight, flat runs, gentle, consistent bends, and adequate stapling. For example: