Can a retail business use social marketing as a competitive advantage?
If you are using the term "social marketing" in its traditional sense, the answer is likely to be no. If you are using it to mean something more like "social media marketing," the answer would be maybe.
Social marketing is typically used to refer to the practice of using marketing techniques to promote a social good. This would be something like using marketing to encourage people to wear seat belts. A retail business would have a very hard time gaining a competitive advantage from this.
If, however, you are talking about the use of social media to gain a competitive advantage, there is a possibility. A retailer would have to manage to gain a competitive advantage by having a presence on social media like Facebook or Twitter. It would have to manage to in some way distinguish itself from its competitors, making itself look "cooler" or more "hip," perhaps. This would be difficult to do if the retailer did not already have such an image.
So, depending on how you are using this phrase, it may or may not be possible. However, it is not likely in either case.