In most cases, the answer is "yes", you can pursue covenant violations as one owner against another. You have all agreed to comply with the covenants, and normal provisions are that both the owners and the association can sue to enforce the covenants.
That being said, there are probably a few things you need to do before filing a suit on your own. One, ask the Association if the owner has any kind of leasing permit. Most association documents allow the BOD to grant hardship leasing permits even if all regular permits are used up. If the BOD issued a hardship permit to the owner, there is no covenant violation. Next, check your documents to see what they say about legal fees for pursuing a covenant violation. It could be that the covenants give the Association the right to recover attorneys fees for covenant violations, but the same rights may not be given to an owner filing the same type of suit. Next, make sure you have put in writing, preferably to the unit owner and the association, your demand that the leasing restriction be enforced. Next, check on the title to the leased unit and compare the provisions of the covenants. The way most leasing restrictions in the merto Atlanta area are drafted, there are several legal ways the restriction can be avoided. IF the unit owner is using one of those legal methods, there won't be much you or the association can do. Finally, if you want to pursue the case, you would be far better off finding an experience community association law attorney who can handle the case. Leasing restrictions are tricky enough that lack of experience by your attorney can cost you in results, particularly since Georgia Courts are not particularly friendly to leasing restrictions and will very strictly interpret the language of the restriction.
This answer is for general purposes only, and it does not create an attorney-client relationship.