Unfortunately you'll need a copy of Destiny during that time to play. However, all the content people are going to play will be available to you on the 15th as well. Also, you won't need the demo if you've purchased the Legendary edition. You'll get the game, The Dark Below, House of Wolves, and The Taken King with the Legendary edition. Make sure you delete the demo before the 15th since there are sometimes issues when you have both the demo and game.