Short answer. No.
When a tree, or anything, falls, and when it impacts, it sets up vibrations in the air. Sound is what a person's mind interprets these vibrations as being.
Think of it this way. If no one is looking at a painting, it still exists, but, it's nothing more than a bunch of smears of colored stuff on a wall. When a person looks at it, their mind integrates it into a coherent whole, and interprets it as a work of art.