Possible? Yes! (depending on quite what you will accept)

Go into the application where you created your cover art and make a note of the RGB values for the background you used.

Then click on your cover in the thumbnails at the bottom of the BookSmart window to make your cover active.

The click on the Backgorunds icon at the top of the page. Then in that dialogue choose More Options. In the subsequent window choose the RGB tab and enter the RGB values for your background.

That will do a little more than you asked for. It will set the background colour for the whole of the cover, not just for the spine. You cannot choose a different colour just for the spine.

Will that do?

......Tony