Following on bbbb's post, I disagree. I started the thread "Why didn't Luther convert to EO?" The results of which convince me that if Orthodoxy had been maintained, the reformation would've been unnecessary.
Orthodoxy is a rather meaningless term here and it gives that sense that the Catholic Church was like the Eastern Orthodox at one time. That never happened. The Catholic Church didn't leave (eastern) Orthodoxy just as the Orthodox didn't leave (western) Catholicism.
When both sides were in communion there were differences, as there had been since the beginning. Not differences in faith as much as practice.
The reason the east and west became so split had more to do with the fall of the Roman Empire in the west than theology and practice. The Roman Empire did not fall in the 5th Century, despite what people commonly think. It actually survived in the east as the Byzantine Empire. The 'barbarians' took over the west and established different kingdoms. The east believed that Christians should be united under one empire with one spiritual and one temporal leader (a patriarch and a emperor). The west converted the barbarians to Christians and formed different Christian states, which the east didn't like.
As the centuries went on, the west became more powerful and the east was losing it, until around 1000 when both were pretty equal. The split happened because of a fight over how to provide common defense against groups like the Lombards, the pagan tribes and the Persians.
The paradox was that the eastern church favored national churches with their own leaders while the western Church favored a single Church with a ultimate leader... quite the opposite of the original temporal setup.
As far as Luther, had any change in time occurred, we can say that he would never have been born, since the world would be dramatically changed.
We really have no idea what would have happened. It might have been that the Pope would have less influence over the western Church, or had more influence over the east and west. In either case, the Church would still have a lot of power, money and influence. In the west, the result was the Reformation, in the east, the result was communism. Both sides struggled with socialism and peasant revolts and potential ones during the 19th Century.
The world could be socialist by now, or Muslim.