Well, as the Arbites are drawn from the Schola Progenium, which evaluates all candidates for psychic potential, I'd say the idea of a psychic Arbitrator is unlikely.
However, I would say it's entirely reasonable that sanctioned psykers could be attached to the staff of a precinct, although they'd likely not enjoy the title of actually being considered an Arbitrator.
Basically, I'd treat it much like sanctioned psykers are attached to the Imperial Guard - watched very carefully, used sparingly, and not actually considered part of the normal structure of things.
Of course, you certainly mustn't let me talk you out of writing any such article. I'd like to see the idea of sanctioned psykers explored further so that psyker background might advance further than "was picked out of the Blackships" or "was found by an Inquisitor before the Blackships got there".
Both are getting pretty tired, and it would be nice to see more psykers who were actually doing some other job before the Inquisition turned up.