Well, just like everyone else is saying, it hasn't crossed my mind. To be honest with you, I haven't even tried any social links on this site yet and I doubt the site has any such function that can enable one achieve the said subject.
Going back to the question, I have to give it to you, it's quiet a good idea, one that can really boost the sites awareness. But I doubt it's going to work as it seems to violate some of the stated rules of this site. Just like someone stated below, every answer, reply or commenting activity has to be done in-house. Hence, sharing a post to gain more thanks and drive more traffic from social media won't be possible. I wish the admin could make this a possibility as i believe it can really work for the best.