I've downloaded a book in ADE on my Mac. I've installed OverDrive Media Console on my iPhone 4 and authorized ADE there. With my iPhone cabled to my Mac, I start ADE on my Mac and the iPhone does not appear as a bookshelf.
ADE does not recognize any of the Apple's devices, and to transfer content you will need to use iTunes. I don't know if this will work with Overdrive app, and if it doesn't you may want to try the Bluefire Reader instead.