On Windows and Linux, java.awt.SystemTray.isSupported() returns true. It also returns true on Mac OS X running an ordinary Java program. However, if you're running a JavaFX program, SystemTray.isSupported() prints

java[93497:e03] [JRSAppKitAWT markAppIsDaemon]: Process manager already initialized: can't fully enable headless mode.

and returns false.

Furthermore, when I close the main window, java segfaults:
# A fatal error has been detected by the Java Runtime Environment:
#
# SIGSEGV (0xb) at pc=0x000000010a4de7f6, pid=93554, tid=140735109491040
#
# JRE version: 7.0_04-b21
# Java VM: Java HotSpot(TM) 64-Bit Server VM (23.0-b21 mixed mode bsd-amd64 compressed oops)
# Problematic frame:
# V [libjvm.dylib+0x49a7f6]

and the Mac pops up a window with some sort of dump (attached). Problem is easily demonstrated by creating a new JavaFX project in NetBeans, and adding a call to java.awt.SystemTray.isSupported() to the start method.