Hi Angelika,
I have seen my
chickens eating half decomposed wood. I am pretty sure I
feed them
enough, but I am not sure if there are any nutricients for them in the wood. But I can't imagine dropping lots of (fresh) twigs and branches into the chickencoop would make the composting much faster.
Making good quality charcoal is maybe too much effort, but if you burn a pile and drop
water on it before it burned completely, you will have charcoal and ashes, good enough to put on the garden soil. The coal will help to keep moisture.
Or you could just make a wall of branches like a
fence? I did this, and like this the branches are at a spot where they don't bother me, and in a couple of years I will have some compost from it!