It's a tough question indeed, at least in the sense that it's difficult to chew on. Your example is a good one; I don't know that one needs to know about the progress of Orwell's illness to appreciate 1984*, and in fact having that knowledge might skew one's interpretation. (At which point we risk detouring into the question of whether or not, or how much, the artist's intent matters to the audience's experience, and whether or not, or how much, it should.**)
What about C.S. Lewis? Or—egad—Stephenie Meyer? Does knowledge of their religious backgrounds color one's readings of their work? Can they be properly enjoyed without this knowledge? (Or is this just an excuse for me to mention that my niece wrote her senior honors thesis in English on the Twilight series as Mormon allegory?)
I think it can be illuminating, for sure, to know something about the circumstances in which a work was created, if not necessarily the artist's biography. I'm suddenly thinking about Woody Guthrie, although I was going to say that knowing that Arthur Miller wrote The Crucible as allegorical to the McCarthy hearings makes it much more interesting than the deadly dreary play we suffered through in high school.
Do you need to know the history of the premiere of The Rite of Spring to enjoy and appreciate it in performance? Or what was going on in Italy when Verdi wrote Nabucco? Maybe not, but I do love me some program notes. Was I glad to know before I started reading that history of a particular New Deal program that the author was a Libertarian blogger? (Answer: Yes.)
*It seems to me that much is often made of the tragic illnesses of various poets and how they're reflected in the work, but I wasn't paying much attention during those classes, as you know.
**There's another essay idea for you, free of charge.
