In a word, no. The word "bedouin" refers not to a culture, but specifically to the desert dwelling nomadic or semi-nomadic peoples of Arabia. By extension you might apply it to the associated settled members of bedouin tribes but that's not really how it should be understood.

Without a doubt, the Bedouin feature prominently in the cultural life of Arabia and the wider Arabic-speaking world both before and after the conquests. This is largely for a couple reasons. In pre-Islamic times the desert nomads were often able to dominate settled towns into paying tribute, and the bedouin who did so occupied the highest positions in the social hierarchy of pre-Islamic Arabian "nobility." Secondly, the bedouins cultivated and were regarded as experts in the most prominent Arabic cultural forms, particularly poetry and song, but also in the belief that the Bedouin spoke the purest and highest form of Arabic. This made them an authority on Arabic grammar well into the middle ages, where grammarians would seek them out to recite poetry or on sentence construction and so on.

After the conquests, and going into the medieval period when CKII is set this in many ways becomes romanticized, so you have poets in the Abbasid court writing poetry about or from the perspective of desert nomads, even though the poets in question lived the pampered life of a medieval poet of Baghdad.

While this cultural influence was pervasive, it hardly "wiped out" all other cultures. While Arabic would enjoy primacy as the language of scholars throughout the lands of Islamdom in the medieval period, there was also a renaissance of Persian culture starting in about the 10th century, exemplified by Persian-language literature of Ferdowsi, Attar, Tusi and others.

The relative power balance between Arabs and non-Arabs after the conquests arguably started to shift much earlier, however, and indeed it's been proposed by some that the Abbasid revolution itself should be viewed as a kind of proto-nationalist revolt by the mawali, the non-Arab muslims, particularly in Perisa. I personally don't quite buy into that but the point stands that non-Arabs gain a renewed socio-political strength after 750 and the Abbasid empire is arguably less "Arab" focused and more "Islamic" focused than the Ummayads were.

The Persian "renaissance" that I mentioned earlier may have been accelerated by the political decline of the Abbasids. After the Anarchy at Samara (861-870), non-Arabs and particularly Turkic tribes come to dominate the political heartlands of Islamdom, which was formalized in the Buyid and then Seljuq sultanates' supplanting the Abbasids as political rulers and reducing them basically to religious figureheads.