According to this article, production started April 1. Assuming that it takes 1 to 2 weeks for the first cars to make its way out of the assembly line, the first cars should be shipped soon. Other interesting nuggets in the article: 160 pre-production cars were built, some will be used as demo cars for dealers, but most will be scrapped. Most engine parts are made in Europe. The DCT is made in Japan. Tours of the plant will be available for customers, including test-drives at the TRC.
http://www.autoblog.com/2016/04/12/acura-nsx-honda-ohio-factory-autoline-video/
http://www.autoblog.com/2016/04/12/acura-nsx-honda-ohio-factory-autoline-video/