The answer of course, depends greatly on definitions of "sound." Well, being a philosophy question it depends on a great many definitions, at the very least the definitions for "if," "a," "tree," "falls," "in," "the," "forest," "with," "no," "one," "around," "does," "it," "make," "a," and "sound." Absurdly pedantic? Terribly. But that's what happens when you try to play definition games in philosophy.
That all being said, the conclusion you arrived at actually is the exact same conclusion philosopher Alan Watts arrived at. This excerpt from one of his lectures bears a remarkable similarity to your argument:
If a tree falls in the forest and nobody is listening, does it make a noise? The answer in terms of modern science is perfectly clear, that the falling tree creates vibrations in the air and these become noise if and only if they relate to an eardrum and to an auditory nervous system. Sound is not something that exists in the external world, sound is a relationship between vibrating air and certain kinds of biological organisms. And therefore it is these organisms which confer what we call sound upon a vibration which in an earless world would make no noise.