Answer:
In my Opinion the Fall of Rome was NOT a major factor in the East-West Schism. However, it can considered one of the many factors that lead to the eventual division.
Step-by-step explanation:
If Rome had not fallen, it can be argued that the Roman Empire would have been much stronger and religious differences might have been tolerated or even controlled with a State religion.
However, apart from Rome, major christian centers in the East and West had completely different interpretations of the law. In the coming centuries, it was as much of a political divide as a religious divide with many Eastern Churches claiming to be founded by the Apostles, while the Catholic pope tried his best to exert his own influence on different states.
Hence, while the fall of Rome might be one of hundreds of contributing factors, it is by no means a 'Major' factor.