In case of DHCP, all you have to do is tell the Adtran to use the DHCP on the WAN interface. Once the IP is learned from an upstream router, the Adtran will also learn the default gateway and automatically set the default route to the gateway obtained from the upstream router. You do not need to populate any default routes in Adtran's configuration when using DHCP.
For example (using CLI here), if this is your gi 0/2 config:
#sh run int gi 0/2
interface gig 0/2
ip address dhcp
media-gateway ip primary
Then the route table would look like this:
#sh ip route
Codes: C - connected, S - static, R - RIP, O - OSPF, B - BGP
E1 - OSPF external type 1, E2 - OSPF external type 2
IA - OSPF inter area
Gateway of last resort is 192.168.2.1 gig 0/2
S 0.0.0.0/0 [1/1/0] via 192.168.20.1, gig 0/2
C 192.168..0/24 is directly connected, gig 0/2
I do not have any "ip route" statements in the running config, so as you can see, the gateway of last resort was populated by the Adtran automatically. It would work the same in the case of a public DHCP address also.
Hope this answers your question.