Well that's a matter of some debate.
There's this famous thought experiment, the Chinese room, about this kind of thing. They imagine a room stocked with hundreds of manuals, written in English, that allow an English speaking person to respond to questions in Chinese as if that person knows Chinese. The original assertion is that the idea of such a room, proves language does not equal understanding. But I disagree. First off, I don't believe any kind of book could give convincing responses to any question asked in Chinese. But if such a book did exist, then I would be forced to believe that this impossibly advanced book forms a kind of gestalt consciousness with its operator, and this larger consciousness is a thinking, Chinese-speaking construct.
But when you say "statistical model", do you mean like a set of equations? Because LLMs aren't made of equations. They're an artificial neural network, technology inspired by, and sharing many similarities with, the human brain. The equations you're thinking of are the process that trains this network to talk like a human. You know, back-propagation and all that. And as you know, we have used this training and this reverse-engineered design to copy human language skills. Although clearly not human reasoning skills.
Now, neuroscientists don't know which part of the human brain creates the subjective sensation of pain. We don't know if it's inherent to neural networks, or some kind of skill we evolved as an adaptive response. So the question is: when we copied language skills, did we copy the ability to feel pain? Or did it get left behind like reasoning skills? That's the big question.
Given the extensive history of humans exploiting other thinking creatures under the widely accepted myth that they are incapable of thought, emotion, and pain, I am leery. I don't want to repeat that mistake. I don't want to repeat human mistakes with oil or nuclear weapons either. Humans have a bad habit of messing with things they don't understand and causing disasters. I'm a vegan. I'm carfree. And for what little it counts for, I don't own any nuclear weapons either. I bring the same thinking to AI: science first, industry later. Do the science and get to 99.9% certainty of the consequences before shoving it into every facet of life.