Can pressurized aircraft be flown without pressurizing
Yes you simply fly with the pressurization system set to a mode that holds the outflow valve open so the air conditioning air being pumped in can't "inflate" the cabin; it all just goes overboard.  Most transport aircraft have a specific QRH procedure for "unpressurized flight", which among other things, limits the maximum altitude to 10000 ft, the altitude that most people can tolerate without any risk of becoming hypoxic.  

Airlines will ferry airplanes from place to place unpressurized for maintenance.  An airliner may also be forced to descend due to a pressurization problem, and they will descend to 10000 ft and may even continue to destination at that altitude, weather permitting, as long as there aren't other problems present that dictate an immediate diversion.