According to Oregon Administrative Rules, "The taking of driftwood in small amounts by visitors for souvenirs, for personal use, or as gifts is permitted. The removal of large amounts of driftwood, or any wood with mechanized loading equipment, shall be prohibited except as approved by the park manager... No wood shall be removed which is inbedded in the beach or in sand dunes banks."
Ask the Oregon State Parks staff for certainty... but I think so.
Thanks! Your answer is awaiting moderation.