There is no evidence that there was any significant Christian population in the Hijaz itself, or anywhere in the Eastern Arabian peninsula for that matter. Actually, despite traditional Muslim narratives, the Hijaz seems to have been almost uninhabited, archaeologically speaking, until well into the conquest era. This is an area of considerable archaeological research at the moment.
The only evidence of any significant Christian population in the Arabian peninsula itself comes from the extreme Southwest corner, adjacent to Ethiopia, Najran specifically being the center. Christianity also penetrated the Nabatean region of Arabia in the North quite early. But the early Christian churches were intensely hierarchical, operating in communion with other churches and the church hierarchy. There is really no good evidence of 'hidden Christians' within the Arabian peninsula itself. Interestingly enough, there is almost no evidence of any Jews within the central Arabian peninsula itself either, despite the fact that the Qur'an's context clearly includes a substantial Jewish population! Hoyland wrote a recent article on the subject, and it is amazing how little evidence there is, and how geographically restricted that evidence is (almost entirely NW Arabia):
https://www.academia.edu/9659736/The_Jews_of_Hijaz_and_their_Inscriptions
This is part of why modern scholars tend to think Islam generally may have originated in a much more Northern context, such as the Nabatean region, than Islamic tradition contends. There is a strong trend to reject the idea of Islam emerging within the pagan central Arabian peninsula.
One confusing factor is that people wrongly think of "Arabs" who lived "in Arabia," but the actual situation involved a vast array of different peoples speaking a vast array of different Central Semitic Arabic-ish dialects extending from Mesopotamia through Syria through Jordan and all the way down the middle of the Peninsula, until they met the Ancient South Arabian languages (which, confusingly, had no relation at all to Arabic). All of these people outside the Arabian peninsula itself were still seen and called "Arabs," and many of them were Christians in the pre-Islamic era. It is quite possible that much of the Qur'an derives from such Northern Arabic Christian contexts -- this is a great puzzle that scholars are working out.
The reknowned scholars of the Islamic era were virtually all Central Asians (many Christians/Jews), and the reason is very simple: Because Central Asia was already a glorious center of world civilization prior to Islam, whereas Arabic speakers were a fairly marginal and illiterate lot by comparison.