If you are going to expose, as it were, a literary Achilles heel, it had better be in some part of your intellectual anatomy that will not lead to pain or social embarrassment. Hypothetically, then, you can probably get away with never having read The Waves but might be ill-advised to confess an ignorance of Pride and Prejudice. Without Qualities you will, of course, dive into The Collected Works of Thoreau, etc etc. Civilisation is all about the successful organisation of hypocrisy, but the more you look at this tricky subject the more you realise that your average book conversation will, as likely as not, be based on bluff. One of the secret reasons why some people read Sunday book reviews is to be able to talk knowledgeably about books at parties.
Universities are quintessentially havens of literary bluff and counter-bluff.
From memory, the plot turns on the fortunes of a visiting American academic who, in his desperation to win the game, admits to never having read Hamlet, with disastrous consequences for his career in the English faculty. With minor Shakespeare, however, it's probably almost honourable to own up to never having read, say, Henry VIII or The Two Noble Kinsmen. Paradoxically, such an admission could suggest a deep scholarly intimacy with Coriolanus, King John and The Sonnets. Nevertherless, I certainly wouldn't go as far as one of Slate's US campus correspondents who merrily claimed to have taught Julius Caesar having only 'rented the Marlon Brando video'. One plausible line of defence that might, or might not, work for medieval poetry, is that you have never been able to 'get into' a particular book.