This would work for an ad shown on ChatGPT and then clicked on (or in the ChatGPT app).

But it would not give ChatGPT information about which other sites are visited.

Of course there would be non-cookie options like fingerprinting (also via IP) that would allow tracking non-the-less.

So you might be talking with OpenAI about your marriage problems and then based on the IP the OpenAI ad network would start showing ads for divorce lawyers on unrelated sites you browse to that display ads.

The solution to that would be using a VPN.