Acids have no effect on wood. They primarily attack ionic compounds and considering that cellulose is not ionic (being a covalent bond), it wont be broken down by the acid. Breaking down cellulose requires some kind of cellulase (enzyme used to break down cellulose, hence being an "-ase") which is primarily formed by single cell organisms, which snakes most likely lack).

However it should be able to pass through the snakes digestive system, it will come back out as what it started as, or will just be vomited up.