Yes, the song as collected from Georgia Turner and others was set in New Orleans. The versions, however, came from the Appalachians.

Ted Anthony, who reseached the roots of the song, wrote, "I originally thought the song was OF New Orleans. But when you listen to the verses- "DOWN in New Orleans," "going BACK to New Orleans" - you realize it is from an outsider's perspective. Many of the early versions seemed to point back to the Appalachian tradition."
Of course, that is opinion based on his take of the song, its singers, and the locale of its collection.
Did the first singer of the song just pick New Orleans, or mean some other city but wish to disguise it- who knows. I think Anthony's opinion is interesting, although it is no solution.

Ted Anthony, "Chasing the Rising Sun: The Journey of an American Song." Simon & Shuster.