Some did, but not all. I understand that Saudi propaganda claims there were no Christians living there before Mohammed. My sister and her husband lived in Saudi Arabia for four years and spent a lot of time exploring in the hinterlands. Out in the middle of nowhere, they found the remnants of an ancient church that had recently been uncovered by blowing sands. Christian symbols carved into the structure left no doubt what it was. There is a lot of history that remains to be discovered beneath the mountains shifting sands.
Before Islam, the Saudi area was conquered by the Sind, a polythist pagan group from southern Pakistan. Islam was a "Third way" between Christian Faith, Jewish holiness, and pagan pilgrimage.
The Quran and Hadith were written under later caliphs to provide Arab rulers enough "wiggle room" to justify their conquest, and permit them to enjoy the fruits of conquest.