In the west, Latin became a daily feature of religious life for everyone, even if they couldn't to more than listen to mass.

The architecture remained and much of it continued to be used, if repurposed. Last year at The Open University there was a conference in included panels on The legacy of the Imperium Romanum in European culture from Classical Antiquity to the rise of the European superpowers (1st century-19th century CE), and "the idea, and performance, of empire as inspired by ancient Rome was less obvious outside the Western world," so the organizers of the conference assume there is enough evidence for the reception of Rome to put several scholars in conversation with each other about it. Shakespeare, when he got his hands on a translation of Plutarch Lives, and many of the references he makes assumes the audience already knew what he was talking about. Maybe the play Pyrimus and Thisbe in a Midsummer Night's Dream can be read this way - it's funny because it comes off like a parody. I don't know enough about the clientele of the Globe to say if it was restricted to an educated elite, but it seems pretty clear Rome remained present in European memory to a significant extent.