even though the entire planet is one, big literal warzone, are there any Arbitrators on Armageddon?
Thank you for your inquiry.
Of all the planets under the protection and watch of the Judge Above All, only one to my knowledge lacked the presence of the Adeptus Arbites. This planet was Cadia.
Even when an entire planet has become a warzone, there must still be someone there to ensure that the Lex Imperialis is being followed. Yes, commissars exist to enforce rules and regulations, but they are concerned with mostly enforcing Astra Militarum regulations. Even a commissar is not above the Lex Imperialis, and so the Arbites must be there.
Arbites Precinct-Fortresses also frequently serve as the first and last lines of defense for a planet, as they are well fortified positions that can be used as a stronghold by loyal imperial citizens and leaders in case of emergency. The Arbites themselves are also highly skilled combatants, meaning that they can serve a defensive force in a pinch. As such, I would not be surprised if the Adeptus Arbites were among the first to fight the greenskins on Armageddon, or if they still have to step up to fight the Ork menace when necessary.
Of course, I must note that this is partially speculative. I am stationed on Atoma Prime, and do not exactly have time to send requests for records regarding Armageddon to the sector fortress. We have enough to deal with on our own.