Regardless if there was an official link, it is probably true that Bitcoin really took off when illegal/quasi-legal enterprises like Silk Road started using them. That's not to say Silk Road created Bitcoin or that all Bitcoin commerce is illegal, just that it would never have grown to real prominence without it.
No, it 'took off' when the media discovered it, and the fact that Silk Road commerce was conducted with Bitcoin gave them the sauce for the story - but the media would have eventually discovered Bitcoin with or without Silk Road.
The market will not necessarily support what is good for society, it will only support what is profitable. This company was even given a head start by the government and still couldn't make it. It's very unfortunate that the destructive libertarian argument that the government should stop spending money and let the private sector work it out seemingly has so much traction.
Is it possible that "green" solutions that are not economically sustainable, and/or that are produced by poorly managed companies may not be "good for society"? Someday a well-managed company will produce economically viable "green" solutions, and the market will definitely support them. The problem with the government spending big money betting on companies like this is that, even if the government is right about which direction we need to go in (which they frequently are not), they still don't know how to pick the right companies to lead in that direction. The market does, and will - if the government lets it.
Are you having fun yet?