Briefly, no. In chronological order, the Persians were conquered by Alexander relatively quickly. This was only after a series of Greco-Persian conflicts that began in 547 BCE with Cyrus the Great's conquest of Ionia and ended in early 330 BCE in with the surrenders of Persepolis and Susa to Alexander after his final defeat of the Persian army at Gaugamela the previous year. The fall of the Western Roman empire has been mulled over by generations of historians beginning with Zosimus in the 5th century and most famously by Edward Gibbon (The History of the Decline and Fall of the Roman Empire, pub 1776). There is rough consensus that it took approximately 320 years to be completed and many agree that the fall was complete on September 4, 476, when the last Western Roman Emperor, Romulus Augustus, was deposed by the German chieftain, Odoacer. The Eastern, or Byzantine Empire, continued to wax and wane until the fall of Constantinople to the Ottoman Turks in 1453.
I read the history of the period known as Classical Antiquity (The Greco-Roman world centered on the Mediterranean) for years before becoming even more interested in how the end of Mediterranean-centered civilization set the stage for the Middle Ages and the eventual rise of Western Europe. This has not made me any better at playing Civ.
