At its basest sense, a forum is a social network, no matter what its intended purpose. People meet, exchange ideas, make connections/friendships/etc.
With that said, I think the most integration I would want to see is the capabilities to log in/register with the major Social Network credentials (FB, Twitter, LinkedIn) and give people the capabilities to share a post on their favorite social network site. I have GH set up to allow people to register/log in with Twitter.
As far as pushing stuff automatically over to a Social media/Network site, I think that would be better served as a modification package.
I wonder how many other forum software packages are starting to embrace the concept of allowing people to log in/register with their social media accounts. Guaranteed that vBullcrap is on the verge of doing that if they're not already doing that.