No, the Nashville was not chartered into U.S. Navy service. The Confederates who witnessed the incident couldn't identify the ships- all the ships piling up at the entrance looked like a one fleet to them. They had good reason to believe the size of the fleet was large, given that they knew how many ships were chartered but did not know where all of them were going because it was a two prong attack, one to Charleston the other to Pensacola.

David