Legal Question in Real Estate Law in Georgia

Usually no. The city will likely have soverign immunity (something you and your fellow Georgians voted for a few years ago to prevent such suits). And most city ordinances shift most of the burden for plumbing issues to the homeowner.

Now the good news. If you bought good homeowners coverage, and didn't try to save money by leaving off coverage for sewage, you'll be covered and they'll fix it.