I doubt there's any property of human-level intelligence that's inherently unreachable by machines. The question is whether GPT-42 would actually be tremendously advanced, or whether we're close to the limit of what the architecture can produce.

The consensus among experts I've read is that known architectural limitations make the GPT-n series unlikely to scale beyond "sounds very human if you don't question it too closely". Algebra, to pick a concrete example, is something that there's reason to believe the GPT-series can't learn effectively - the output generation mechanism is fundamentally incapable of looping or recursion, which severely limits how well it can break things down into subproblems.