Ehhh I think that argument is weak. For one, the adoption of Christianity as the state religion happens a good deal before the collapse of the WRE. Second, the underlying issues that cause the collapse don’t have much to do with Christianity (the empire outgrowing its administrative capacity, reliance on conquered peoples for the military, power games in the capital, constant juggling of where the troops are stationed) and many of them were present before Christianity got adopted. Third, and perhaps most critical, the East doesn’t collapse and continues to function under Christianity and, later and farther east, Islam.

Not to mention that the “dark” in dark ages refers to the relative lack of written records in the West in the era compared to late antiquity before it and high medieval/renaissance after it. Most of those records being written by bishops, so said records are skewed towards a religious viewpoint.