Not the general release of Gpt4 as available in chatgpt plus (it will tell you as much if you ask about recent event) . The plug in version apparently can access the Web but that is hard to get access to.
Bing can access the Web but the results are a bit random.
Former times I used to add a robots.txt entry to some of my own websites whose content I didn't want to appear in the internet wayback machine. Unfortunately, it does not longer work that way today.
User-agent: ia_archiver
Disallow: /
But now, there is also something comparable to exclude ChatGBT that should work.
For newer content, it is possible to block Common Crawl. Since 2008, this non-commercial organisation has been creating a copy of the internet, which it makes available free of charge to researchers, companies and private individuals. This huge database accounted for 60 percent of GPT-3's training data. To prevent the database from tapping into your texts, all you have to do is change the robots.txt file of the website and add the instruction:
User-agent: CCBot
Disallow: /
A third case is plugins that complement ChatGPT. OpenAI explains that you can also block them by editing the robots.txt file with the statement:
User-agent: ChatGPT-User
Disallow: /
The directive can also be modified to exclude only certain parts of the site or to explicitly allow plugins to collect content from the site, OpenAI says in its documentation.