a piece of oak wall panel would not have enough buoyancy to keep them both out of the water, it was just barely floating high enough to keep Rose out of the water. If he'd been able to climb aboard the piece of debris would have swamped and they both would have froze to death.
In fact I'm calling bullshit on the Mythbusters that
Chukzombi
posted after watching it because their piece of debris was swamped with both of them on it and they would have frozen to death before being rescued if they'd been in the same (fictional) situation as Rose and Jack.