The issue is getting people to click on your website, why would any one do that if the entire content is already extracted by the ai, which directly gave it to the user?
Is your website more pleasant to use than ChatGPT/Bard/Bing Chat? Some actually are. Websites can load fast, be responsive, beautiful and well thought out. Those websites are a treat to visit.
However, if you need to first dismiss a GDPR waiver, a request to know your location, a request to show notifications, a chatbot that is available right now for a free sales consultation, and a request to subscribe to a newsletter; and once you do that, the page jumps around for 30 seconds as the ad auctions finish and obtrusive video ads flood in, and when you try to exit the page your back-button is hijacked; then the answer is probably "no".