The pilot reported that during a multi-engine check ride, the check pilot (examiner) simulated an engine failure. When the throttle was retarded, the landing gear unsafe warning horn came on and it sounded throughout the remainder of the flight. The pilot performed a simulated single engine approach and decided to delay extending the landing gear until the airplane was on the base leg of the traffic pattern. While turning to the base leg, he was distracted by calls from other traffic and failed to extend the landing gear. The examiner also reported concentrating her attention on the other traffic. The airplane touched down with the gear up and it slid about 1,400 feet before coming to a stop. The airplane's fuselage sustained substantial damage. The pilot reported no preimpact mechanical malfunctions or failures with the airplane that would have precluded normal operation.