Numerous people have done it (check out CrazyGuyonaBike for some journals. I did it (East>West) a few years ago. However, I actually rode along or near the coast from Perry, FL to Galveston, TX. Doing Galveston westward in early April.
The coastal route definitely has more traffic than the ACA route but was quite doable. I road the west side of the Mississippi from NO to BR due to lower traffic counts and quieter roads. In NO, be sure to cross the Inner Harbor Navigation Channel up next to Lake Pontchartrain as the other crossings would be suicidal. There is a nice sidewalk/bike path along the beach in the Gulfport/Biloxi area also.
Lots of services once you are in Mississippi. Be sure to check on campgrounds ahead of time as several do not accept tents (ACA should use it advocacy for that!). Lots of hotels but most are not inexpensive.
Hope you have an enjoyable ride. John