Actually the simple answer is no. They can however ask you to remove it from the property if they discover it. If you refuse they can press criminal trespass charges. They can also fire you since Georgia is an "at will" state. The "at will" means you are employed at the will of the company and at your will. Either can terminate their will at any time with or without cause. The not so simple answer is yes because if you wish to remain employed by that company then you carry at the risk of your job.
In sum, employer gets to dictate its rules on its own property.
Same goes for every other "right." Let us phrase the question another way. "Can my employer stop me from having a gay rights parade in the parking lot?" It's a first amendment issue, right? Well, the long and short answers Seajay gave would be exactly the same for that question, although I suspect these days more employers would be friendly to the second question than to the first.
Why? Because they are more poitically active than gun owners.
They can only search if you give them permission. In some cases this is also a requirement of employment. Depends on what they had you sign when you went to work for them or since you have been working for them. The best way to handle it is if you decide to carry to work just don't tell anyone. The only reason they would even bother you is if they wanted to obtain an excuse for your dismisal anyway. I'm not sure if I would want to work there if they had it in for me anyway. I can't tell you to carry or not to carry. Only to carry at your own risk of being fired.