One potential problem is that in Christianity, God is much more powerful than the Devil. D&D otoh presents a dualistic world where either the forces of good and evil -- terrestrial and cosmic -- are evenly matched or evil has the advantage. Admittedly, within Christianity there have been varying perceptions of the extent of Satan's power and influence on earth. 2 Corinthians 4:4 describes the Devil as "the god of this world."Again, I'm not proposing turning demons and devils into gods. I'm going for more of a Judeo-Christian "God vs the Devil" feel, rather than D&D's usual polytheistic approach.
In a world where Christianity is the true religion polytheistic faiths could still exist. Their worshippers might be deceived by demons, as Christians have claimed.