So far no has even touched on the original question.
It is a good question and I do not know the answer. I would bet it would also be illegal even while the building is under construction. The property would belong to the school system and school maintence workers are usually involved, especially in the final stages. I've been teaching nearly 30 years and have been involved in moving into 2 brand new schools as well as a couple of major renovations.
Regarding Georgia law and schools. It is still technically illegal to have a gun within 1000' of a school but there are some strange and contradictory laws. In GA it is perfectly legal to drop off or pick up your kid with a gun in your car. It does not matter if it is concealed or in sight. You may not bring it into the school or park your car with a gun. As long as you just drop off and keep moving it is legal. An employee cannot have a gun in their car. It is possible to get permission from the principal. I have done so in the past to provide a gun for a lesson or demonstration.