Yes - easy peasy
In fact any twigs touching the ground from your fallen tree may have rooted already. I would use longer cuttings to get more of a leg on the plants, but it depends what you want them for. We used willow as hedging stakes one year and in spite of putting them in upside down so they wouldn't sprout, they still did
You can use any size of twig or branch too and one inch thick ones make a sturdy plant more quickly than a skinny one. Another way is to stand the cuttings in a bucket of water for a couple of weeks until the root buds just appear, then plant them out. It's best not to let the roots grow long as water roots have to be regrown once planted out. For planting out, you can put them in a slit trench all in a row then transplant them the following year, or if you can protect them you could plant them direct where you want them to grow.