Absolutely! I rode this way for years. A milk crate is fine; I actually preferred a wire basket obtained from my LBS - I think it was designed for a handlebar basket. Attach it to the rear rack with zipties, put a small bungee across the top, and you're good. Just drop your regular backpack in and go!

I have since moved to the Arkel Bug for commuting, as I was looking for a bit more stability provided by keeping the weight (laptop, textbooks, clothes, lunch) at axle-height. It is a very nice pannier and an ok backpack - no waist strap for instance to heavy loads are awkward as a backpack. Not very many functions like internal pockets either.