This is a fantastic new article (out of what seems likely to be the dominant text for many years on Late Antique Roman-Arab relations) on Arab Christianity in the Sixth Century. Borderline mandatory reading IMO for those interested in the milieu where Qur'anic composition arose.
https://www.academia.edu/7806301/_Christianity_and_the_Arabs_in_the_sixth_century_in_G._Fisher_and_J._Djikstra_eds._Inside_and_Out_Interactions_Between_Rome_and_the_Peoples_on_the_Arabian_and_Egyptian_Frontiers_in_Late_Antiquity_Peeters_2014_in_pressIt breaks the Noldekian dogma that Arab Christianity was largely limited to the advances of the imperial-backed church hierarchy. "However, the increasing importance of non-Chalcedonian confessions meant that Christianity could be de-coupled from its Roman associations, and take on other forms of political significance in the hands of both the Persian shahs and the Arab rulers themselves."
And I would add even more significantly (since I see ur-Quranic composition as a form of monastic anti-Chalcedonian rebellion against 'corrupt' church hierarchy), here are the concluding sentences:
"But we should also be prepared to an even broader range of ‘non-state actors’ in our imagination of the process of conversion. First among these are the missionaries and their hagiographers, who selected patrons who could sponsor religious adjudication or patronage after being rejected in the Roman world. In return, their Arab patrons might cease to be ‘barbarians’, unworthy of a political voice, and become ‘orthodox’, bastions of true belief set between ‘heretical’ or ‘pagan’ persecutors. Secondly, we should also remember that subordinate Christian Arab groups, of whom the ʿIbād of al-Ḥīrah are examples, might also be agents in the process of Christianization, and play a role in accelerating the conversion of their kings and communicating the event to their co-religionists."