Using the example from /usr/lib/x86_64-linux-gnu/qt5/examples/widgets/desktop/systray on the MATE (Gnome2 fork) desktop on Linux no system tray icon is shown.
There is also no message that the tray is not supported, so AFAICT Qt5 thinks it is supported, it just doesn't work.
This is a regression from Qt 4.8.6, where the system tray example works, and the Heart icon is shown.
The system tray on MATE also works for all other applications that I use (Pidgin, the mixer, networkmanager, etc.).
FWIW the notification popups work (also they appear to originate from the Pidgin icon).