Does X-Windows have to be installed on a Linux-box in order for Java to display fullscreen graphics?
Well "fullscreen graphics" is a bit vague.
Anyway, apparently there is a an effort ongoing to access the framebuffer from Java: Framebuffer Toolkit.
The objective of this project is to produce a body of code which is a lightweight framebuffer-based peer implementation for AWT and Swing. The goal of this code is to remove the dependency on X or other graphics layers such that graphics can be redirected to a framebuffer (e.g. a raw buffer, VNC, etc.). This example implementation will prefer pure-Java solutions, with public extension points available to enter native resources as necessary.
See Project proposal: fbtoolkit.