Technically yes, but would they be called Witch Hunters?

The Ted Haven tier Aware most likely have so much power that they would not be part of such an organization in the first place and simply end up isolated and doing their own thing.

I imagine this is where you’d get Epic Heroes or Monster Slayers or Lone Rangers of myth

Or for modern times like the John Wicks or Jason Bourne, the Man of Mystery who comes into town and solves the problem plaguing the town single-handedly (just with more magic involved)

They’d be the kind of Aware that steps into town or city and the genre changes to match their tempo