Swing IS supported using JOGL_AWT or LWJGL_AWT...
Using JOGL_AWT, Swing painting is not supported. There are big differences between the rendering of AWT (heavyweight) and Swing (leightweight) components.
First of, all mixing AWT and Swing components is a "no go", as this is officially stated by the Java community. As JOGL_AWT does not seem to be lightweight, it is not Swing and will not support Swing. This is one major issue found with the way JOGL_AWT will draw the 3D canvas. If there are overlapping components or components in layers above the canvas - the glass pane of the underlying JFrame might be an example -, they don't draw correctly. Even if you don't use transparent colors at least drawing the background of any Swing component, which is not opaque, will not yield expected results. As an example: an empty JPanel in the glass pane would make the canvas invisible, instead some default background color will be painted instead.
Therefore, JOGL_AWT will neither behave like, nor support expected Swing behavior.
Although Swing classes are subclasses of AWT Component or Container, they aren't AWT components.
My latest experiments with Java3D Swing canvas yielded much better performance compared to the latest Xith3D releases even with AWT rendering chosen. My conclusion: Swing rendering must not necessarily be slow. It is slow, if it is implemented the way to be slow.