get your assumptions right first, then prove.
strictly speaking, yes the does fall, because first you have made the assumption. and on that assumption you can safely say when the tree makes contact with the ground, sound waves are produced, whether it reaches a human's ear is a different matter.
if you want to leave it open, you would say we are not sure whether we heard the sound of a tree falling or not, from that you cannot exactly say if the tree fell or not.