I have been doing this now for a while, not every night of course, but particularly when my wife abandons me and I am left home alone at night. Once in a while, the content finds its way into my dreams but not as often or as obviously as when I am listening to reruns of Art Bell. I have a few different audio versions of the Bible and others are available via streaming. Even when I don't recall any dreams that are inspired by the Bible, I think that it puts me in a good frame of mind.
I still continue listening to the Word at night with my headphones too. And have extended this to the day time when I am at home and I will play a DVD that reads the Word to me while I am going about my house work, cooking, etc. I can definitely say that God's Word is saturating our home with His presence and His peace and my spirit feels more peace no matter what is going on around me too.