The answer is a simple 'no'. The end of the Western Roman Empire in 476 was a complex event and should never be explained monocausally. The empire was indeed largely Christianised and I'm sure many people were influenced by their Christian beliefs, but its impact was never as all pervasive as Gibbon suggested many centuries ago. Modern historians emphasise the role of 'barbarian' migrations, internal Roman conflicts and many other contingent factors. Lastly, the Eastern Roman Empire was obviously not destroyed by Christianity - it lasted until 1453, so anyone arguing for this view would have to explain why Christianity only caused the fall of half of the empire.