Yes, very much so. We have Roman epigraphy (carved writing on things like tombs etc.) dating back to the Early Republic, a good 3-400 years before the transition to the Common Era. We know there were literary works by Romans throughout the Republic, but it's in the Late Republic that we start to have literary sources still preserved - think Cicero's time onward. Indeed, the Augustan period (just before Jesus' birth) was a flowering of literature sponsored by the Emperor - Livy, Horace, Vergil, Ovid and others wrote extensively during this period. Rome had extensive contact with the Greek world from the time of the Early Republic, and thus also gained contact with Greek literary traditions, especially after the conquest of Greece. (Some more conservative Romans viewed this as a bad thing, since Greek literature and learning was seen as un-Roman). By the Late Republic and the Empire (when Christianity began and spread) all elites - the senatorial classes, local elites, etc. - would probably be literate in Latin and Greek.

Source: SPQR, by Mary Beard

(out of curiosity, and without any judgement: what led you to ask the question/wonder if Rome had a literary culture prior to the spread of Christianity?)