If there is an alliance with the Byzantine Empire (as in your proposed POD) that's easy, at least friendly relations are desirable.
And it depends on the time period, of course. I mean when there were pagan Scandinavians which, I guess, more preferable than the Christian Europeans (but I might be wrong here).
But, ye, it's doable with right people in charge of this process and steady financing.
I am not sure about the benefits from using the Pechenegs though.
You see, the Pechenegs are the Turkic mounted warriors and the Abbasid mamlyuks are the Turkic mounted warriors, which makes it easier for them to feel common group solidarity and ally in the palace struggle.
This feeling 'us and them'; 'us' being here 'the Turkic mounted warriors' and 'them'... well, everybody else.
It depends on the century, but it seems that you get mostly Christian and pagan mercenary through Byzantium (or through Europe). That might become a problem for the Muslim Abbasids and might cause some discontent among the local Muslims.
By the way, what about using local free-born (non-slave) non-Turkic, non-Arabic Muslim population as a power base for the Abbasid army - Iraqis, Iranians etc?
I mean there were some local groups whose martial qualities were quite good; they might be a nice supplement to the Abbasid Varangian Guard, giving the caliphs some additional space for political maneuver, playing different army factions against each other.
The Pechenegs may be similar to the Turkic Mamluks held in the Abbasid hegemony. Yet, they are also quite removed from the Abbasid source which was on the fringes of the then and former Tang Dynasty. Typically, Turkish warriors or children captured by the Arab muhjahadeen on the fringes of the Islamic world who waged intermittent war with the Turks for slaves. Those raised as Pechenegs in the Pontic Steppe would be living in Iraq as warriors for hire and distinctly Pecheneg. I would not see why they would even want to associate with what is still a slave caste.
The local Muslim cannot do anything nor have a say. They already loathed the Mamluks, but not due to them being foreigners. It was due to their overbearing attitude that was projected, it was as if they forgot their place in society (in that era's mindset). Despite this, Arab society for good or better is well acquainted with exotic non Muslim holding odd jobs throughout the realm. The more classic example though is African slaves used for any number of uses as opposed to Europeans. For instance, I would tentatively doubt that a majority of Zanj slaves in Iraq were Muslim, possibly a vast minority. Though, I can imagine the Arab society in Baghdad mistaking these Europeans for slaves.
Abbasids are limited in their use of Arabs, Iranians, Kurds, Egyptians, etc... Islamic fiqh has strict regulations upon conscription when not in war time. Any break of this would truly draw the ire of the Islamic community who see themselves as dependent upon Allah, not the state. Arab warriors for hire or jihad, went to the fringes of the Islamic world to seek glory, loot and rewards for jihad, not to the palaces of Baghdad to live a calm life. Iranians likewise, were migrating to the fringes to wage war against Turks or Hindus, why work in Baghdad when such lucrative loot awaits just outside the Islamic world? The other aspect too, is adventure. We in the modern world tend to forget the allure to young men born in an impoverished village to yearn for adventure and challenge. Baghdad/Samarra for such men, quickly becomes a prison...
The other reason, the Abbasids oddly, do not trust their own people. Abbasid power began by crushing the Arab elites who represented the Umayyad and Syrian camps.
This is why the Abbasid turned to slave castes to begin with.