Some context about this here: https://arstechnica.com/information-technology/2023/08/openai-details-how-to-keep-chatgpt-from-gobbling-up-website-data/
the robots.txt would be updated with this entry
User-agent: GPTBot
Disallow: /
Obviously this is meaningless against non-openai scrapers or anyone who just doesn't give a shit.
The possibility exists, though I wouldn't hold my breath.
https://arstechnica.com/tech-policy/2023/08/report-potential-nyt-lawsuit-could-force-openai-to-wipe-chatgpt-and-start-over/