When user enters a prompt, the backend may retrieve a handful a pages to serve that prompt. It won't retrieve all the pages of a site. Hardly different from a user using a search engine and clicking 5 topmost links into tabs. If that is not a DoS attack, then an agent doing the same isn't a DDoS attack.

Constructing the training material in the first place is a different matter, but if you're asking about fresh events or new APIs, the training data just doesn't cut it. The training, and subsequenctly the material retrieval, has been done a long time ago.