No, I don't think Konoha has Hunter-nins either.
If someone leaves the Village just like that, I think the Hokage simply selects a few of the ANBU to hunt them down. Basically they get the job of a Hunter-nin that way, but they're still ANBU.
So they probably don't have hunter-nins as ranks, but I think it's sort of like a mission. A hunt-mission or something of the like.
It does makes you wonder about Konoha... Perhaps it's just too peaceful and they trust their own villagers too easy.
Maybe Tsunade will make Hunter-nin teams, since Sarutobi was too careless.. I bet Itachi could leave Konoha with ease.. as did Sasuke... are there more known missing-nins from Leaf Village?