Proven? I don't think so. I don't think there's a way to devise a formal proof around it. But there's a lot of evidence that, even if it's technically solvable, we're nowhere close.
Indeed; it definitely would show some promise. At that point, you'd run into the problem of needing to continually update its weighting and models to account for evolving language, but that's probably not a completely unsolvable problem.
So maybe "never" is an exaggeration. As currently expressed, though, I think I can probably stand by my assertion.