Forming an LLC for Primary Home Ownership for Privacy
In a past we answered a similar question, and I invite you to check it out: Owning Real Estate in California with Wyoming LLC.
In short, technically one can own a property in an LLC, registered in a state different from the state where the property is physically located. However, the moment your property is used for commercial activity, such as renting, or is sold, the LLC would need to be foreign qualified in Georgia.
For privacy protection I would actually recommend New Mexico LLC instead of Wyoming or Delaware, due to special anonymity benefits provided by NewMexico LLCs, making them favorite tools of asset protection specialists. I invite you to read my answer to the following question" "Best state for anonymity?".