Does "close window" mean "close application"?

The Gossip folks say that they'd like this explicitly noted in the HIG.

http://lists.imendio.com/pipermail/gossip-dev/2004-April/001241.html

Gaim (with the System Tray Icon plugin activated) has the behavior that the
application seems to live in the notification area, and one can create and
destroy the window with impunity, never affecting the life of the application. 
That is, when the window is visible, clocking on the close button does not cause
the application to quit, it merely removes the window from the screen.  The
"handle" for the application is then the icon in the notification area.

Gossip (and Rhythmbox, et c.) places an icon in the notification area also, but
takes the approach that clicking close makes the application behave like every
other application -- quitting the program.

Gaim's behavior is very attractive to me.  (Indeed, I am accustomed to it
already and rely on it.)  It's similar to the "hide" functionality of
GnuStep/NeXTStep/MacOSX, except that it may be seen to violate the consistency
of "close".

My personal idea:  Create a fifth kind of window control, "hide", exclusive to
the absence of a "close" (and "minimize"?) and also exclusive to the presence of
a notification area icon which is willing to control the invisible application.  It