I mean, objectively, yeah, it seems that stones and related objects shouldn't have a thread. But they can be destroyed by balefire. They can be affected by ta'varen.

I'm not sure if I can argue that they can play a role in the whole "destiny" aspect of the Pattern, though. But as a random example, say a rock rolled off the side of a mountain, causing a rock slide that blocked a narrow pass and forced a person to go back to a village where that evening they saved the life of a drowning child who would one day become king. Is the stone part of the Pattern? Or did some rock rabbit thing, more likely to have a thread, have to cause the rock to fall because the rock is not part of the Pattern?

I'm not sure.