The chickens haven't bothered any of our new trees (200 in the area they forage in). I don't see that tree leaves are anywhere close to a preferred food. There's a ton for them to eat otherwise and they help mightily on grasshopper and earwig control. Alfalfa, clover, those plants do get eaten, especially in early spring.
I'd say try it and observe closely the first few days. Maybe plant some goodies to emerge a couple weeks before turning them loose. The trees should have a good growth spurt that will put them out of harm's way rather quickly.
Now geese, that's another story. They will "bill" a tree to death just for the entertainment.
I've found that chickens are much more likely to disturb the roots of young trees by digging than eating leaves or buds. Scraps of fencing laid flat on the ground around them, or piles of sticks and brush, are a good and usually free deterrent to the scratching. Once the trees are over your head it shouldn't be much of a problem.
Rocket Mass Heater Plans: Annex 6" L-shaped Bench by Ernie and Erica