No, BookSmart does not let you place an image on the spine of your book.
The cover layouts in BookSmart offer a variety of templates with text containers on the spine, but image containers are only on the dust jacket flaps and front/back covers. There are no templates with full-bleed options for the spine or the flaps.
Matching the background color of the spine and flaps to the predominant color in your images, as we show below, can create a continuous look from the front to the back of your book.