On Windows, you can close Blender when it is minimized to the Tasktray. You can close the program by right-clicking and selecting "Close Window" of by clicking the "X" on the thumbnail while hovering.
Unfortunately this doesn't work if the "close save" dialog comes up to prompt for saving changes. The prompt pauses the quit process but you can't tell because it is just drawing on the minimized window. In a nutshell you can close Blender this way if there are no changes, otherwise it seems to just do nothing.
This patch alters the message handling on Win32 so that on message WM_CLOSE the application will restore if minimized. This has no negative effect if there are no changes as the program just exits normally. But if there are changes the program is restored and you see the "save close" dialog so you can answer the question.
Unfortunately I couldn't find a more general way to handle this, rather than for Windows only. Events are queued while minimized but they don't seem to be processed while in that state so couldn't find a way to restore the app at a higher level.