The setting does exactly what it says to be honest:
- It hides your profile from public view (admins, mods, and yourself can see it)
- It stops the presence feature from showing when you’re typing in a topic
As far as stats go, someone could go count all the posts and likes you’ve made manually. I’m not certain what the privacy concern is here. If a user wants anonymity on a site for their actions, admins can turn on anonymous posting mode, which the user can enter so that activity isn’t associated.