No, I do not think he can "cure" this by healing CPs. Just as effects from Critical Hits are not removed by healing your Critical Damage. 

Armour of Contempt reduces the number of CPs gained from any source, and can reduce this total to 0. If you roll on the shock table, and it says "Gain 1 CP", then a person with Armour of Contempt gains 0.

Darth Smeg said:

Hm, OK. Regarding Armour of Contempt and the gaining of CP you are absolutely right. My question is more to the part of the talent that you can ingore your accumulated CP as a Free Action for a round (not sure of the exact description). That might help for Faith powers, but the rule was written long before Faith power were part of the game. Just wondering what it is good for to ignore you CP for a short time…

Huh, never realized that before.

"In addition, you may Test Willpower as a Free Action to ignore the effects of your accumulated Corruption for one Round." says the fine rulebook.

I have no idea what this might be useful for.

Edit: Perhaps you could use this to avoid the penaliy given on the Malignancy test?

Ie, You just got your 61st CP.  You succeed on a WP test, and now you don't get the -20 to your WP test to avoid a new malignancy.
Not too sure about this, it kinda runs in the way of Dark Soul, no?

As for the Arbiter that got the CPs and failed a malignancy test…i have a few ideas and standards that i use in our group ( and has thus far worked well )

First…i DONT give a simple reroll by burning a fate point like normal.  Whenever one of my PCs burns a fate point..they AUTOMATICALLY make the save by the minimum needed ( skin of their teeth kind of luck ) to avoid whatever it was they needed to. As for getting rid of some of the malignancies…a visit to a tech priest Medicae and loss of appropriate few hundred XP AND thrones AND downtime for the priest to perform the necessary transfusions/lances/sterilizations and skin grafts/transplants to take care of any physical issues and the appropriately trained psyker to get inside their head and "straighten out" or otherwise "shield" them from similar issues in future ( IE anything they have seen to date…wont cause any futher mental trauma due to barrier wards placed by the psyker - similar to what they do TO psykers on Terra to make them more stable mentally..obviously this wont be cheap or easy or fast to do..but it is a possibility for a trusted throne agent who has proven their value to their Inquisitor. ( unless the Inquisitor is a puritan in which case…PC is toast ) 

Note: the equivalent XP i require ( to represent the time and dedication to treatment the PC undergoes ) if they actually want to try and remove a malignancy ( once they have removed enough CPs…to reduce the level OF taint ) is a flat 1000XP..denoting extensive time and preparation and execution…I can see you playing this out one of two ways..(1) The time and XP spent once their "threshold" for CP is lower than the test that caused the Malignancy in first place…then they spend the 1000XP to give them a WP test or T test ( depending on whether the malignancy was mental based like nightmares or such or physical like wasted frame or poor health etc ) IF they pass this new test ( taken at same penalty as the regular malignancy test ) then they have beaten the malignancy through whatever methods used…Obviously this will require the PC to devote ALOT of time and XP and thrones to this ordeal ( and it should be ) in order to get rid of something so serious…but it is better than the lazy way of saying..youve got it now your stuck with it forever without hope…cmon ..really…always a chance…OR (2) The PC spends the XP and thrones and automatically gets cured ( treatments successful )

Second..while there are some malignancies on the table in the DHCB pg 239 that could be an issue in general..some of them are actually not bad like Dark-hearted..an affliction i can easily see working for any seasoned Arbiter..all that death and gore and waste..does take its toll. Same as the Hatred one…all that is the equivalent of is a Talent you would otherwise pay for…only difference would be that id say the GM and PC should work together to determine just WHAT is the object of that new hatred ( could easily be the cause of the malignancy in the first place..like cultists or xenos-eldar etc ) something that makes sense around the time the malignancy happens…The Fell Obsession one …hell that just described death cult assassins penchant for morbidity…the same as the Morbid result i could rule for a very large portion OF death cult assassins…Distrustful isnt that ad to have..esp not in this universe..lol might keep the PC alive a bit longer…Bloodlust..perfect for any feral worlder to regularly START with..given the description and some of the details on the planets ingame…Strange addiction could easily also be tied in with both morbid AND fell obsession if the PC was a death cult assassin..or simply pretending TO be to cover up their malignancies…( hint hint )

what's a halo device?

is it a drug injector? I remember there being a drug named halo…

While there indeed may be a drug called "halo", I currently have no recollection of any such thing. 

What I do know, however, is that there is a rather comprehensive section on Halo Devices in DH:DotDG, pp 96-103.

In short: it is an archaeoxenon device of mysterious origins named for its place of occurrence (this includes both the Scarus, as well as Calixis sectors). It bonds with its "user" over time, transforming the "user" into an increasingly alien thing that eventually loses his human nature (and in the process acquires a tremendous ability to defy death).

so the machine is sort of a "sell your soul for ultimate power" -thingy?

Yes, sort of, if the "user" doesn't mind his personality and sense of self dissolving into oblivion over time and being taken over by the alien thing. Also, machine might be a big word for it: it comes in various forms, but as a small object that embeds itself in the "user's" flesh.