I don't honestly know that I've ever seen an actual breakdown of population statistics for the region during that period of Late Antiquity. It's not a region we have a lot of documentation for in that time period - Marshall Hogdson, in his very encyclopedic and detailed tome The Venture of Islam laments that "On the Sasanian Empire--and generally on the Fertile Crescent and Iran in the thousand years before Islam--we are more poorly informed than perhaps on any other major lettered historical period." (vol 1, p. 141, fn. 17).

It would also depend on what you mean by "predominantly." Different Christian groups combined probably amounted to over half of the population, but I would hesitate to state that Pre-Islamic Iraq was "Christian." Most histories of the region stress the linguistic and religious diversity at the time of the Islamic conquests.

We're usually given to understand that it was a mishmash of Zoroastrian, different Christian sects (many of which had been excommunicated by the various Christian ecumenical councils and so hopped the border into Persian territory where they were tolerated), Jewish, and smaller Persian religions (similar to the Christian sects, these were not officially tolerated by the Sassanids and found shelter in the difficult to navigate environment of Iraq's mountainous north or marshy south).

Fred Donner, in The Early Islamic Conquests starts with Zoroastrianism, the official state religion, which did not dominate but was practiced mainly by the Persian elite in larger towns.

Donner asserts that "The Nestorian Christian community may well have been the single largest religious community in Iraq on the eve of the Islamic conquest," (pp 168-69) but gives the impression that they were a plurality (i.e., the largest single group, but not constituting over 50% of the population, so not a majority). He then goes on to state that the next largest community was Jewish; and then lists about eight other religions and sects that could be found, but doesn't offer a more concrete sense of what percentage of the population these groups were.