It wouldn't be tied up in court that long. On election day, by Georgia law, the electors were chosen by the voters. At that point the slate of electors is set; confirmed by the counties, the Secretary of State, and the governor, all as the law mandated. Suddenly, based on their own suspicions and in violation of the law, the legislature says they are going to appoint their own slate of electors. How long do you think it will take for the courts to throw that slate out?
I would hope the answer is never.
I would hope the court would say that this very scenario is spelled out in US Code Title 3 Chapter 1 §15 and would step back and let Congress sort it out according to established federal law.
-PJ