This user's profile page on Meta and Stack Overflow shows the website as plain text and not a hyperlink - this is by design, and fine in this case. But the profile page on Stack Exchange shows a real clickable link.
Another example I salvaged from my flags history - this is an old user, so it's not a matter of caching any potential rep.
This is sort of inconsistent, I think the website link should also be plain text on Stack Exchange for users with no rep at all anywhere.
At least part of the Stack Exchange profile page on are indexed by Google, as well as the site profiles. But the link is marked
nofollow (regardless of rep). So it might be less than a problem than I thought.