Yep, just make sure it has a month or so under really good cover before you burn it, or dry it out near the stove for several days. That wood in the pic may produce slightly less heat than perfect wood, but it will still heat great. Much of the White Ash I get is about like that.
That, and the mess it makes! But having said that, I keep it most of the time. Good wood, bad wood, it's still wood and is still burning in the stove.
One good think about oak, there is very little sapwood. Even if it all gets punky and falls off, you haven't lost much. Most of what I heat with has some punky sapwood, burns great.