Partly accurate, but misleading.
Draper and White argued that science conflicted not with “religion” as they understood it, but only with traditional Christian theology. White’s title is explicitly about the “warfare of science with theology in Christendom.” White regarded himself as a liberal Christian of sorts, but really defined his faith by borrowing the words of Matthew Arnold about there being a power, “not ourselves, that makes for righteousness.” Draper hated Catholicism, especially for how it had often been closely tied to secular power in many places, such that orthodoxy was enforced by authorities. The notion of “intrinsic intellectual conflict between religion and science” is a harsher form of the conflict thesis, endorsed not by Draper and White but by some modern scientific atheists, such as Coyne, Dawkins, Weinberg, and the late Victor Stenger (God disturb his soul).