It's mostly just silly, there are some British cultural references but it's not classics except Holy Grail being a long reference to the Arthurian legend.
Whilst you can enjoy most of Monty Python without a high-brow education, as you'd somewhat expect from a troupe made out of graduates of the two top universities in Britain, there are several sketches that are only funny if you have read Proust (summarize Proust competition) know some Latin (romanes eunt domus), or know the most famous English poems (ant poetry reading) etc.
They only ever use these things as set dressing from what I've seen - you could substitute Proust for any overly high-minded literature, the centurion is just being pedantic about the graffiti and so on.
Yeah, I have no idea who Proust even is, and the extent of my Latin knowledge is that I can usually spell "per se" correctly, but the centurion scene is still one of my favorites, and the Proust one is worth a few chuckles.
I think you just have to be willing to figure out the context from feel.
Even if you never heard of Proust, you can probably still get a chuckle out the choral society trying to summarize his magnum opus in 15s and never getting past the "Proust in his first book, fa la la". But if you find it already amusing knowing nothing about it, you'd probably find it a bit funnier if you knew that, on the one hand, In Search of Lost time is thousands of pages and takes weeks or months to read, and, on the other, isn't exactly action-heavy. And probably still more if you could relate the attempted plot summaries to the book(s).
And I don't think the ant poetry sketch would be funny at all to someone who doesn't recognize "Look on my feelers, termites, and despair" or any of the other lines and understands none of the Queen Victoria jokes.
