No,the activity will die down significantly. Community sections won't be as active, there just won't be a lot of people around. However, as the gaming changes, so will Sythe.org. When people find a new game to play, Sythe will adapt and become advantageous to players of that game. Runescape will die most likely, Sythe.org won't follow suit.
Why would Runescape shut down? Plenty of people still play it, so I don't see it happening any time soon. If it did, Sythe would pretty much die out also.
I'm sure the activity will slope, however Sythe wont die. Sythe will simply conform to what replaces runescape.
Sythe will change, but not be gone forever. Im sure people will move onto the next game, or just continue to use the other sections.