I had this often growing up in relatives' homes in Acadiana - around St. James, St. John, Lafourche, Terrebonne Parishes. Didn't see it in New Orleans and we didn't serve it that way at home in NOLA.
The November issue of Cottage Living magazine has a good recipe for turkey and andouille gumbo with potato salad. With rice as well - saying that "gumbo without rice is a mortal sin." The only discussion is if the potato salad goes in the middle or on the side of the bowl.
Are there any restaurants in NOLA that serve it this way? Some of my friends from that area of LA still do.