I like reading Shakespeare, Dickens, and Orwell on my free time. But someone today just brought it to my attention that all this is a waste of effort: what does 16th, 19th, and 20th century literature have to do with today's world, or even programming? I couldn't answer that. That comment, and the fact that it's common to ridicule English majors, has made me question how reading literature could possibly be productive, especially for something as objective as programming.
I'm afraid this one will be closed very quickly as off-topic.
I'd say: no, English lit won't make you more productive. It will only make you a better and more well-rounded person. (There, I said it.) I'd rather work with a developer who reads English lit in his spare time than with a developer who spends his spare time learning yet another programming language or reading yet more books on algorithms, design, software architecture etc.
There is more to life than productivity. Just maybe not on this particular site ;-)