Yes... but you'll have to make a special JPanel that will paint the image in the background... and make sure that any JPanels you add to it have setOpaque( false ) set on them so the Image shows through... and make sure to use the Java 2 Plugin to use Swing in your applets!
Here's some code to illustrate an implementation of the JPanel with the background image...
Write once, run anywhere, because there's nowhere to hide! - /. A.C.