I don’t know the Georgia court system, so I can’t give a specific answer. If there’s a higher court to use, my bet is that they use it. Heck, they might even try to get this judge in trouble for overreach of power or something like that.
This hearing is administrative fact finding hearing. It will make a determination based on the facts and present them to the SoS for ballot consideration. I believe as in NH, it is decision that can not be not appealed. But is there is an avenue of appeal it would go to the GASC that is mostly right leaning justices.