No, they must be dead. Also, don't bother poisoning a wood tree for those badges either, because they just drop their planks rather than leaving a dead tree.
So how does a wood die in order to apply toward the badge? Or any other tree for that matter? Or is if just wood trees? I haven't really thought about this badge so far.
I think you get the "Clear" option when you poison a non-wood tree and it dies. It looks like a pitiful wilted stump. You have to remove that before you can tend the patch to plant a new tree.
Thanks. These badges are one of the reasons I bought a large house. So I could have four patches to work toward these badges without bothering anyone else. :) just hadn't gotten started on it yet. So much to do in Ur. :)