Well for me I can say that I created a start-up, grew it, sold it, entirely using "social" media. 

I use the term social here loosely, as I consider the use of it in recent years as somewhat late and misrepresentative of prior art. The Internet has always been social by default, we've always had emails and  forums which are by nature all about being social around arguments and debates. - not to mention chat rooms and bulletin boards.

My start-up was a distance learning school, completely online. We used zero off-line advertising, zero paperwork, zero central offices, zero anything relating to off the Internet, in fact we didn't even use the telephone, and banking was all electronic. 

So for me I can state a resounding yes to your title. - but I would refrain from including the last couple of months/years buzz about social networks (facebook + twitter et all) as being the dogs bollocks of social media, nothing new here really, they all stand on the shoulders of giants.

:)