OK, maybe I was wrong - they did have one NA NSX that ran.
24 Hours of Le Mans
The NSX made three appearances at the 24 Hours of Le Mans, in 1994, 1995 and 1996.
Three Honda NSXs were entered in the 1994 24 Hours of Le Mans. Cars numbers 46, 47 and 48 were prepared and run by team Kremer Racing Honda, with Team Kunimitsu assisting and driving the number 47 car. All were in the GT2 class, and all completed the race, but placed 14th, 16th and 18th.
Three Honda NSXs were entered in the 1995 24 Hours of Le Mans. Honda's factory team brought two turbocharged NSXs which were entered in the GT1 class numbered 46 and 47. Car 46 finished but was not classified for failing to complete 70% of the distance of the race winner. Car 47 did not finish due to clutch and gearbox failure. The third NSX, number 84, was prepared as a naturally aspirated car and run by Team Kunimitsu Honda in the GT2 class. This NSX, driven by Keiichi Tsuchiya, Akira Iida, and Kunimitsu Takahashi, placed 8th overall and first in the GT2 class after completing 275 laps. This NSX was featured in the game Gran Turismo.
For the 1996 24 Hours of Le Mans, only the Team Kunimitsu Honda NSX returned with the same drivers. It completed 305 laps to finish in the 16th position overall, and third in the GT2 class.