I have wondered this myself. Young trees have an astonishing ability to survive being brushhogged, resprouting from the stumps endlessly. But I'm not certain about older ones. I have a male (not fruit-bearing) tree that I've been meaning to try the experiment on, but I haven't had the heart to do it.
Meanwhile, however, there's a lot of variation from tree to tree in exactly how soft the fruit is when it's ripe enough to fall, but most fruit will survive the fall without bursting. And you don't precisely have to wait for it to fall naturally. Except on the very largest trees, you can usually shake the tree with your body enough to dislodge the ripest fruit, so that it falls for you to pick up while you are there and ready (instead of trying to beat the raccoons and deer and coyotes to it).
Sadly I do have one set of trees growing in deep canopy forest where the fruiting branches are thirty feet up and more, and the fruit is larger than usual (the size of good sized apricots) and softer than usual. These are my best-tasting persimmons but they *splat* like a chicken egg with no shell when they hit the ground. One of my long term to-do list entries is to clear out the forest floor (challenging, there's a ton of fallen snags and brambles and other large trees) so that I can plant a bed of mowable soft clover and have room to string some fruit-catching hammocks.
Edit: OK, now I'm laughing. Turns out I asked a version of this same question
four years ago and nobody knew then, either. Guess I should have done the experiment!