Yap it should, note that it uses logs from the bank.
It doesn't chop them on the island (due to the limited amount on the island)
Make sure to disable auto-retaliate to start off.
I still can't promise you it won't get hp/str/att exp ... missclicks on monster can happen
EDIT: (^make sure to equip a bow, but no ammo to prevent this ^)
Khaleesi