A) As of a few years ago, carrying a firearm is presumed legal (same as it's presumed legal to be driving a car) and the absence of having a GWL is an element of the offense (generally.) It's hard to make the case that merely carrying a holstered firearm is 'disturbing' when thousands of law enforcement officers do the same on a daily basis.
B) Georgia does not have a 'disturbing the peace' statute but it does have a 'Disorderly Conduct' statute. There are four very specific behaviors that can be charged as disorderly. If not violating any of those specific four, you are not being disorderly. To me this is very preferable to any generalized, open-ended, subject to the officer's discretion 'disturbance' charge.
I openly carry at my local Publix and Ingles quite often. I have no doubt it caused a bit of concern the first time they saw me do so. They were a bit less alarmed the second time. The third only got a raised eyebrow. Now they don't even look twice and neither does my local bank when I OC there as well.
Oh,... and I should mention the police are not bound by duty to question someone operating in a legal fashion; just as you are not bound by any custom or authority to engage in conversation or answer intrusive questions by officers who are only trying to find a reason to make an arrest. Making a statement that you refuse to answer Any questions and then remaining silent is the surest and fastest way to put an end to questions. Every question you do answer from, "What's your name? It won't hurt to give us your name to put on our report, will it?" to "Did you walk here, or did you drive?" can only prolong the interrogation.