I just tried out the relatively new ability to hide profiles on certain sites, and it turns out that it doesn't really hide anything at all since the hidden profile still has a link to my network account.
Hidden profiles shouldn't have links to the network account at all, this will always break anonymity. Hiding them will leak the information that this is a hidden profile, but this is still far better than the complete lack of anonymity as it is now. The network profile also shouldn't show any hidden communities, to avoid leaking the connection from a non-hidden to a hidden one.
The page where you can hide communities states the following:
Hiding a community means other users will not see it in your Communities list and Top Network Posts. It does not, however, mean your activity here is completely private. Moderators and Stack Exchange employees can see your list of hidden communities. Other people may also be able to associate your presence on those communities with your public list in certain cases (via the API, for example).
This is extremely misleading since it gives the impression that the hidden profile is reasonably private except to moderators or SE employees. The only other compromise it mentions is the API, and even then only in "certain cases".
While the text allows many interpretations, it gives the impression that the major privacy leaks are moderators and some advanced API shenanigans. It doesn't say anything about an easy-to-find link on every profile that completely nullifies the feature.