Tom --
First Company "A" of the 30th Georgia Regiment was the "Butts Invincibles" of Butts County. A man named Francis M. Wise, age 24 in 1860, is the soldier listed in Henderson and the NARA index. I don't find any Confederate military information for your ancestor, who appears to have been too old or infirm for active duty.
I've never heard of a soldier who enlisted under his father's name, but it would be surprising for Roda/Roddy Wise not to have enlisted.