Jambi is a PITA to compile and use, if you aren't on one of {Linux32, Linux64, Win32, Win64, MacOSX}. I still use it for all of my apps, though
Also, Jambi depends on "java.awt.*" in some places so you need Swing support to use Jambi.
Anyways, Swing is implemented using nothing but "java.awt.*" calls, so Swing will work for sure, no worries. (Saying that you get JVM support without Swing is like saying that you get X11/Xorg support without being able to display anything)
EDIT:
@Drack Ever heard of OpenJDK?