AI models are trained relatively rarely, so it's unlikely this would be very noticeable among all the regular traffic. Just the occasional download-everything every few months.
However, the pratical evidence is to the contrary, AI companies are hammering every webserver out there, ignoring any kind of convention like robots.txt, re-downloading everything in pointlessly short intervals. Annoying everyone and killing services.
Just a few recent examples from HN: https://news.ycombinator.com/item?id=45260793 https://news.ycombinator.com/item?id=45226206 https://news.ycombinator.com/item?id=45150919 https://news.ycombinator.com/item?id=42549624 https://news.ycombinator.com/item?id=43476337 https://news.ycombinator.com/item?id=35701565