they will eat apples when they fall, but I have NEVER seen one climb a tree to get em, there NOT that good a climber
I have them in my yard often for 30+ yrs and plenty of fruit tree's here and NEVER seen one in my tree's yet, BUT have seen a few over the yrs climb a tree or two on some farms I worked/been on!
but climbing tree's is NOT the norm for them they prefer mostly wide open area's they can see danger cominga way's off and live in tunnels/dens, or under buildings, they can wreck heck on tunneling iunder buildings and sheds!
SO,they do dig and burrow holes in the ground and they can GO far under ground and wide
MANY farmers have LOTS of isue's with them causing cattle to break legs whe n they fall thru from the surface and its been known to tip over a few tractors too, when they also cave in under ground tunnls on side hills or??
SO yes they can damage your tree's if they dig too close to tree roots and or cause you grief with tunneling
some hard core folks do EAT em, I won't however
they can be trapped trather easy, both live trapped and relocated, and or, trapped and killed
or just shot, most states have very long and liberal seasons on them
COyotes LOVE to eat them, so, if it lives long if you leave it alone, odds are you have LOW coyote numbers in your area!