You can, but it's not very good. Unlike a shovel, you can't set a hatchet as an 'item type' UOA wasn't programmed with Siege's economy in mind, hatchets don't wear out on other shards.
I use a simple 'last object, last target' client macro tbh. Set it to a single key and just hold it down till you get the 'empty' message or till you're close to losing the wood you chop because you can't hold it.