A thought experiment, which I came up with many years ago while studying for my Classics A-Level...
How might Western civilisation be different now had Cleopatra and Mark Anthony beaten the Romans at Actium?
I don't see how this would have changed the timeline on the fall of the Roman Empire. The collapse of the Roman Empire had more to do with over extended resource supply lines than it had to do with politics, armies and whole civilizations for that matter need to be fed and the situation eventually became untenable as the empire reached its peak.
Actually you can attribute a large portion of their failure to the massive system of lead pipes they used for their water supply. To this day their descendants still suffer from the effects lead had on their minds and bodies.
@CheshireWarcat Although that theory is pretty much consigned to the myth bin now, you might read Scarborough's essay on that topic. There are several good reads out there that detail how empires collapse when they run out of energy, be that calories contained in wheat to run labour pools to oil to run machines, when the furnace that drives an empire runs out of fuel the whole system collapses.