Re: So basically...
Yes it makes a noise. "A tree falling in the woods" and "rendering (it falling in the woods)" are the same things. Simply "falling" and "sound" are the same thing, objects moving.
What you mean is, if the game is not rendering the forest, will the tree even fall? That is only knowable if you know the code. Is the tree falling a pre-determined event (in code or causality) or a random event?
If it is random (true at the event unknowable noise), then you never knew it was going to fall, as the forest was not rendered/calculated/simulated. It never falls and you see a tree standing up.
If you are using a pseudo random number generator (or a known algorithm for the random effects) and know the seed, then you can always recreate the event after the fact, without it needing to "fall".
If it is pre-determined and you do not render it, how do you then know where to put the tree after the fact? Our universe see no distinction between "observed" and "not-observed" for ensembles such as trees (though this changes for individual quanta ;) ).
We could retry the question as "if we see a tree lying on the floor, did it fall, or did it appear spontaneously there?" That is a better question to ask.