I really don't think your analogy is a great one there. We can't compare brains to computers usefully because they're super distinct. You're sneaking in this assumption that there is more complexity to the models by implying there's something larger present being terminated early but there isn't.
This seems as absurd to me as asking whether a clock has a concept of time. Being very good at doing time related stuff, vastly superior to a human, is not evidence in favour of having any sort of knowledge of time. I think that the interface of these models may be encouraging you to attribute more to them than there could possibly be.
