LLM’s can still only pass limited Touring Tests. The longer the interaction the worse they do. Which of course means you can easily create an experiment they successfully pass, but just as easily you can create an experiment where they fail.
CAPTCHAs are nearly useless because of how little you need to pay humans to solve them.
A more interesting question is whether there is a Turing test that is easy for ALL humans to pass, while still being hard for LLMs.
In practice, most of the major CAPTCHA vendors already rely on non-privacy-preserving tests for those needing more accessible solutions than a visual puzzle.
Google's audio captcha (only available in a few languages and unusable for those who also have hearing issues) only works for a narrow band of users, not trusted enough to bypass the captcha entirely, but also not untrusted enough. If you fall outside of that band, you get a nice "your device has been classified as a fraud risk, please use the visual captcha" message.
hCaptcha goes even further and straight-up requires you to have an "accessibility cookie", which requires verifying your email address (and apparently your phone number in some cases) to obtain, as well as disabling some anti-tracking settings in your browser.