While the media does help keep a sport out there, and make more people aware of what is going on in that particular sport, I feel no sport, especially professional, really need the media to stay relevant to the world. Mainstreams sport are popular enough and have a strong enough fanbase to thrive without media attention.
Media support sport as much as sport support media. The money made from sports from sky alone is the largest chunk that keeps it going, as well as sky buying rights to sport. Perhaps the sport would survive without the media. But who would promote and advertise games & give the players the financial motivation they need to play a good game?
No, I do not believe that sports could survive without the media. The media coverage of sports is 24/7, 365 now days. The media is able to keep people interested in the sport by hyping up certain games and events. Without the media, sports would be reduced to the local area that they are played and fans from other places would not be able to follow their favorite teams and athletes.