In my experience the background image spreads over all the widgets in the sidebar as if one image is behind several windows. It looks really nice. But if I understand what you are describing, I’d put the image I wanted in a widget at the top of the sidebar and then style that widget to have a transparent background and no margins or padding. For example:
Pam, that’s what is happening here http://www.dbepub.com. All of the book covers are widgets that are styled the way I said above. Of course, as Tom points out my code is overkill. Can you tell I’m not a coder? 🙂
It also works to just put an image link in GP Hooks, Before [Right or Left] Sidebar Content, which might be easier if you are only doing one or two. I did that with the social media icons here. http://www.elt.international
In addition to the plugin Tom recommended, I use Widget Context to put widgets where I want them. Works great with GeneratePress, too.