The definition of what "common knowledge" means is quite a question in itself, but I will assume that it means the educated elite. I have several reasons to respond to your question by the affirmative but not without some limitations. Most of the litterature that is left today were preserved specifically because it was read during the middle ages, even if some text that we consider as highly informative were preserved only by one or two manuscripts. The basics of roman history were nevertheless quite well known. Summaries of roman history, mostly derived from the 146 books of the Ab Urbe Condita of Livy were already made during the Roman empire and while most of Livy is lost today we have quite a lot of copies of some of these texts, like the history of Florus for exemple. Florus is often despised by modern historian for his mistakes and shortcuts, but it follows the greats steps of the roman expansion. Furthemore new adaptation of the roman history were produced in medieval times, sometimes to provide a sythesis over the various authors. The roman empire also served as an exemple for some contemporary states, especially the Holy Roman Empire and the Papacy. Last but not least, a lot of christian martyr took place in modern times. Even if the medieval era had no consideration over the historicity clothings of the characters, this again made the roman empire an unforgetable period in history culminating with the conversion of Constantine. The greek history was not completely forgotten, as it is mentionned through roman historiography but there were no impulsion to learn greek among the few educated people, until the fall of Constantinoble wich bring lots of manuscripts to Italy (the looting of the city in 1204 also had an influence but I have not the expertise to discuss it in further details).