It would be hard.
See, Arabs were in really few numbers in Spain and after the Berber Revolt (and Umayyad takeover didn't helped) were entierly cut off Arab reinforcements (the last ones being Syrians djunds, that couldn't stand Yemenit Arabs anyway).
In order to maintain their power against not only a wholly Berber settlement when it come to Muslims but also a crushing majority of Christians, the power distinction had to be harsh.
It doesn't meant that Muladi (especially Hispano-Romans) couldn't access power, but it was under Arab (and Arabised, Arab culture being the measurement of how much social importance you could hope for) conditions.
I doubt that Arabs would joyfully give up what required several really important revolts (with even reconversion to Christianity) to establish in the Xth century.
Assuming it happens, and not by several revolts (whom some were actively supported by independent Christian, I think that giving more power to Muladi would eventually turn to the creation of de-facto Muladi states as Banu Qasi's, giving they outnumbered ethnic Arabs, and had a more local based power (partially inherited from pre-conquista).
Now, Umayyads certainly became "andalusians" (the term existed, but wasn't ethnicized) : physically, they were close to other south European rulers (Abd al Rahman being redheaded and blue eyed, by exemple), but Arabity remained an important marker probably more than elsewhere in the Islamic West (if not Arabo-Islamic world as a whole) because of the historical context of the conquista.