100% the data you input to the ChatGPT 4 prompt window is being used to train ChatGPT 5, there is a reason a lot of companies are placing bans on it and telling employees to never enter sensitive data.
I sincerely hope that LLMs won’t play a role in search, I don’t need a search engine trying to infer what I “meant” to type, Google and DDG started doing that and pushed me to Kagi as a result. Just take the words I type verbatim and search them in your index, don’t assume this is my first time using the internet.
Models are not trained during inference, are they?
Regardless, it seems like LLMs are going to have some role to play in search in the future. It's just not clear what that role is yet.