A little further research reveals that Nancy and Capt. McConnell were taken as a prize by a French privateer in 1796. The resolution of that case is listed in the congressional record.
Nancy was a small ship, listed at 48 tons. She and Capt. McConnell seem to disappear after 1797. IMHO, the general particulars of this case stand a very good chance of being true.
Curiously, this is another wreck that appears to be missing from the lists of usual suspects. Nancy is not even listed in E. Lee Spence's usually very comprehensive Shipwrecks of Georgia and South Carolina.