Yes, it's possible to have background images in sideboxes.
See one of my sites for an example...
www.edutrade.co.uk
... and here is some of the CSS that governs the appearance of the background image...
Code:
.sideBoxContent (line 617)
{
background-color: transparent;
background-image: url(../images/sidebox_back.jpg);
background-repeat: repeat;
background-attachment: scroll;
background-position: center bottom;
padding-top: 0.4em;
padding-right: 0.4em;
padding-bottom: 0.4em;
padding-left: 0.4em;
}