I could be wrong but I believe this decision is final. The court is a function of the executive branch as is the SoS. As in NH, there is legal recourse for an executive decision.
IIUC, this proceeding was technically only for inclusion on the primary ballot, so unless there’s some law that extends this decision to the general election, this issue isn’t over in Georgia. And to be on the GE ballot, Obama is going to have go through legal challenges to prove his eligibility.