FWIW, personally I think it muddies things to frame the question as if "..using statistical token generation" was a limitation. NNs are Turing-complete, so what LLMs do can just be considered "computation" - the fact that they compute via statistical token generation is an implementation detail.

And if you're like most people, "can cognition happen via computation?" is a less controversial question, which then puts LLMs/cognition topics easily into the "in principle, obviously, but we can debate whether it's achievable or how to measure it" category.