I've brought back small pieces of unfinished wood (larger sticks and chunks of wood), declared it, and after inspection been allowed to keep it. It likely depends a lot on the specifics including origin, species, and state of the wood. I'm not saying you can or can't bring it back, just that the above-cited USDA regulations on wood products are complex and with specific definitions, caveats, and exceptions...pretty hard to state for certain without expertise. You may want to simply contact USDA customer service (below) and find out more definitively:
https://www.aphis.usda.gov/aphis/banner/contactus