That's one piece of the pie. It may very well be the Christianity wouldn't have caused the collapse of Rome if, for example, Rome didn't allow so called 'Barbarians' to settle in Roman lands, among other reasons of course. And you have to critically analyse why Christianity caused the collapse of Rome. It isn't because Christianity intrinsically, as most European countries can attest to, causes nations to fall, it's specifically because of the context of what Rome was, an Empire built upon the divinity of an Emperor, and the importance of the Emperor. Christianity caused the Emperor to lose said divinity, and it also allowed clergy to gain more power over various institutions in the Roman Empire. Many modern historians disagree with Gibbons, instead arguing things such as military spending had a larger part to play.