Alan -
It's quite possible. A lot of Georgia soldiers who lived near state lines crossed over to join units in Alabama and Florida. Have not been able to find out anything else about the Garrison in the First Georgia. I did find a notation of a James Garrison as Captain of Company B, 16th Tenn. Cavalry, formed July 15, 1863, which was part of Forrest's cavalry. Unfortunately I have no information that connects these two. There were several Georgia cavalry regiments that served under Forrest - he could have been in one of those.