I could see them having a fictitious named person to be able to track the bad guys, but other then that, I can't see the value of having one.
I really don't think they would get into a Tweet Battle like the ones we read about on a daily basis.
GCCs are political animals just as much as military ones. Social media enables them to advertise their awesomeness and their beneficial use of taxpayer dollars to maintain world peace. Public transparency is practiced from the BCT level up. It’s just how things are. Otherwise they’re shadowy organizations that suck in dollars for unknown purposes. Even the CIA and NSA have social media presences.