No, it may not be true.
The SecurityManager might disallow you the full screen control. Mainly because one could easily fake whole screen in order to grab a password from not-suspecting user (you could mock a bank website).
It can be false:
- in an applet
- in a WebStart Application
- while running in headless mode
JavaDOC of GraphicsDevice.isFullScreenSupported:
Returns true if this GraphicsDevice supports full-screen exclusive
mode. If a SecurityManager is installed, its checkPermission method
will be called with AWTPermission("fullScreenExclusive").
isFullScreenSupported returns true only if that permission is granted