Device Group using public NAT

Want gtm to sync you don't need to use device groups but need to setup a gtm sync group:

http://support.f5.com/kb/en-us/products/big-ip_gtm/manuals/product/gtm-implementations-11-4-0/3.html

When you configure one gtm setting up each gtm as a GBLB server and configure the translation address as the private IP and the address as the public ip, then do a gtm_add on the other gtm devices to the first ones public ip.