I received this answer to my question from a Georgia PHd who has researched the local crayfish species.
Crayfishes of Georgia | Georgia College
I would personally rather you not introduce any crayfishes into Georgia waters that are not native to our state. The biggest threat facing crayfishes is the introduction on non-native species. Those guys you get on the internet are native to Louisiana, Mississippi, Arkansas, area. They will get out of your pond and into the local waterway. I would recommend buying a few minnow traps or fish traps and set them out in a creek near you and try catching some of the local species. The local crayfish will do as well in the pond as any you could buy on the internet.
One thing to consider that I haven't researched much is the life history characteristics of the Red Swamp Crawfish (the one you can order). During certain times of the year, this species burrows in the ground. I wonder if you had enough that your dam could be compromised. Also, I don't if you want them for your fish, or for eating. The adult red swamps will eat fish eggs as well (and a bream won't be able to eat them). Anyway, some things to consider. Take care.
Chris
Christopher E. Skelton, Ph.D
Professor
Graduate Coordinator
Department of Biological and Environmental Sciences
Georgia College & State University
Milledgeville, GA 31061
478-445-2440