Yes, probably. I think War and Peace would take three months (I'm a slow reader). But, sure, many of the others could be read in a week. I do like the idea of total immersion though. How many of us will ever get that chance? It's sad to think of it, but almost none of us will ever have the time to read even a fraction of the truly great books, and we'll certainly never have the chance to do nothing else for months on end.
I remember the philosopher Bryan Magee saying that he used to do just that. He'd take some great monster, like Schopenhauer's World as Will or Plato's collected dialogues or Dante's Divine Comedy or Darwin's Origin of Species or whatever and totally immerse himself in that one book. He'd go to a cottage in France, with no phones or distractions, and do nothing but read and re-read. In the evenings he'd walk along the beach meditating on what he'd read, and then next day pick up where he'd left off. I'd love that. A book is a miracle. It is the mind/consciousness/inner life of someone at the limits of what it can do. Dostoyevsky's Crime and Punishment, for example, is a great mind getting as deep down as it possibly can (not that I've read it!). Same with Hamlet or Paradise Lost.
Re-thinking it, if I had three whole months, and could devote them to just one book, I'd go for one of these:
Tolstoy: War and Peace
Stephen Hawking: A Brief History of Time (couple of pages a day!)
Proust: Remembrance of things Past
Bertrand Russell: History of Western Philosophy and The Problems of Philosophy (sewn together to make one book)
Oscar Wilde: Complete non-fiction (i.e all his essays and letters)
Richard Dawkins: The Ancestor's Tale
Carl Sagan: Cosmos
Aldous Huxley: Collected Essays
Bill Bryson: A Short History of Nearly Everything (the giant hardback edition)
It isn't so much the time it takes to read the book (you could probably read Russell's Problems of Philosophy in a day if you really went for it), more the opportunity to totally immerse yourself in it – to re-read bits, meditate on them, etc. You know, live that one book. It would also be striking just how much of an effect that one book would have if you spoke to no one and did nothing else but read and re-read it. Imagine being locked in a room for a week with nothing to read but Thomas Hardy, Joseph Conrad and Philip Larkin. God, you'd be suicidal bu the time they let you out. Now imagine reading nothing but Dickens and Jane Austen and P G Wodehouse instead. You'd come out floating on air.