Hi brenski,
I used to have an 800XL (NTSC) with a GTIA chip that couldn't show mode 9, although the other GTIA modes worked just fine. Any game/demo/intro that used mode 9 would give me a strange dark distorted screen that had lost "vertical hold". I remember the intro from Rescue On Fractalus!, which uses mode 9, exhibited this behaviour even though the game itself worked fine.
I had also typed in a GTIA Paint program from an issue of Antic magazine which worked just fine, but I cannot remember (been more than 25 years since!) if it used mode 10 or 11.
I think there is also a location you can POKE to see if the GTIA is working as expected however you'll need to search for it, or perhaps someone else can reply to your post.
Regards,
Mani