No. You don't get to the Mac OS X desktop or even the boot DVD user interface. What you describe is nowhere near that far. The OS needs to load a driver to support rendering the more complex objects that both the desktop and the DVD installer use. The "GFX0: family specific matching fails" may mean the graphics hardware is no longer recognizable to Mac OS so it will not boot to a desktop or a GUI installer. I don't see anywhere that you said you saw any icon or object that resembled as such. The hard drive and DVD icons are what you see if you hold down the option key BEFORE booting an OS, something that doesn't require the full features of a graphics driver.
Not sure were you're getting the part about getting "to the Mac OS X desktop or even the boot DVD user interface" I don't recall saying that. To the contrary, I've been saying all along that I can not get that far. But earlier someone suggested the graphics card failure to which I replied, how would I be able to get to a graphic mode [not the full blow OS] where I can choose which drive to boot from? Here's what it looks like, but without the wifi bar below:

But if I understand what your're saying, that the graphics card may still be able to dispay simple graphics like the one above, just not power the entire OS?