Georgia law on run offs is wierd but this is a federal election and that statute is preempted https://thecivicscenter.org/blog/2020/11/6/young-people-could-decide-the-georgia-runoff-races-for-us-senate
These state law sources say that the runoff is a continuation of the general election and that only those who were registered to vote in time for the general election can vote in the runoff. If that was the end of the story, then the 23,000 young people turning 18 after November 3 and before January 5, as well as all the people who were already 18 but simply did not register before the general election, would be completely out of luck.
But there is more to the story.
The National Voter Registration Act prevents states from maintaining a voter registration deadline longer than 30 days in advance of a federal election. Federal law overrides Georgias state law provisions that would otherwise prevent young people from registering now to vote in the runoff in January.
This is not just a hypothetical answer to an unresolved question that the courts will have to decide at some point in the future. The issue has already been decided through a lawsuit brought by the Georgia State Conference of the NAACP (represented by the Lawyers Committee for Civil Rights Under Law) in 2017. The judge granted a preliminary injunction preventing Georgia from maintaining a deadline more than 30 days prior to a runoff for federal office, and the state accepted the ruling and signed a consent judgment obligating the state to follow federal law in the future.
The Georgia Secretary of State recognizes the force of this ruling and has marked December 7, 2020 as the deadline to register in order to vote in the January 5, 2021 runoff election.
These young people can vote if they register before December 7 even though they may turn 18 after December 7 but before the run off day