Try it and see. The big stuff can be piled on the side of the road, while the leafy/branchy stuff would go on the road itself. As it dries out and as you drive over it, it will breakdown.
One thing you'll find is that as you pile up the mulch, the soil will become more permeable beneath, which will greatly increase water infiltration. So while you worry about heavy rains carrying that material away, what you may find is that instead, you'll get much better infiltration and less run-off.
I create brush piles below my fruit trees on the hillside. I throw the large branches down first and create a kind of organic terrace. Particularly on south-facing hillsides, it keeps the sun from baking the soil on the downhill side of the tree. The soil temperature stays much much cooler, the soil retains moisture better, it creates a fantastic habitat for lizards, snakes, fungi, microbes and other living things, and eventually, that organic material breaks-down and feeds the soil. Take your time and lay the branches down, building a kind of "beaver dam" of branches on contour below the trees.
I agree with Tyler: never burn anything organic. Even slow to rot stuff like osage orange, use it somewhere. I can never get
enough biomass and I've only got a fraction of the
land you have.
