Not really.
It's a fact that the Emperors in the East were far more effective in governing secular and temporal affairs in Constantinople up till the atrocity of 1453, whereas in the West the Emperors were usually ineffective absentees who spent the bulk of their time in Milan rather than Rome. By the 500s the emperors in the West were gone and there was a complete power vacuum with various localized lordlings in dozens of shifting alliances.
One sign that the Empire in the West was weak or nonexistent was the absolute lack of claimants to the throne after the abdication of Romulus Augustus in 476 - who just gave up on the office of Emperor rather than defend himself militarily.
The Roman nobility petitioned the Eastern Emperor to appoint a replacement, but he refused because the Romans had overthrown two of his previous choices.
From 395 to 771 (376 years!) there was no effective ruler in the West and from 476 to 800 there was no nominal Emperor.
For about 40 years (775-815) there was centralized political leadership, but by 850 the West was in political chaos again and wouldn't see any true stability until around 1250 when France had strong kings and Germany had strong Emperors again.
So from about 400-1250 there was no effective political center in Europe except for the brief Golden Age of Charlemagne's reign.
And even then, it was 250 years of shifting alliances around a French-German rivalry followed by the Reformation and yet another outbreak of political chaos.
The Eastern Emperors and the Ecumenical Patriarchs enjoyed a close, symbiotic relationship for centuries with only brief episodes of animosity - the Popes experienced the exact opposite state of affairs.
The unproveable part is that it allowed the Roman Church to operate in the "genius" of the Church.
It could be just as easily argued that the survival of the Eastern Empire allowed the faith there to flourish in a way that was not possible in the chaos of the fall of the West.