Short answer, yes.

Although Latin was the primary language, a good portion of the ruling elite could also speak and write Koine Greek. Latin was the state language and was spread through the empire due to its importance in government and trade. The other people's in the Empire still spoke their local languages so there was a need for documentation and translation.

They have epigraphical evidence of translations from Punic, Coptic, Aramaic and Syriac. The Celts and Germanic tribes had little In the way of written examples, though there is some documentation of various Celtic dialects. The Germanic tribes left even less than the Celts, the only Germanic language that we have evidence of through the Romans is the Gothic language.

Once the centralized government started to fall apart, Latin began to evolve into the Romance languages, so there is evidence of the evolution of the language.