Yes exactly! Its what happens naturally, trees dies, falls, takes others with them with the fall, make space for newer trees and wood decompose... Natural succession.

If you don't have woody material, just leafs works too, the key is organic matter build up and photosynthesis. So we tend to cut weeds (when they start to mature/flower usually) very cleanly for them to grow bigger and better, not killing them, focus is to build soil for more demanding plants.