No, it doesn't hide the links and this has been discussed recently in another forum.
I've made a designated hack that extends the show_description feature and allows me to set the activity to display the link (and icon) only in editing mode.
It should be possible to achieve the effect by css. The technique is to hide by default the activity links and then reveal them by means of a block that is set by permissions to be available only to authenticated users.
The quickest way to see how this works is the following.
In the summary of the frontpage topic add the following css in html mode (you may need to turn the editor off in your user profile):
<style type="text/css">
.pagelayout-frontpage li.activity{display:none;}
</style>
(You can also add this css definition in your theme)
Then add an html block (if the above css is in the summary the block must be in the right column) and in its backend html (editor off) enter
<style type="text/css">
.pagelayout-frontpage li.activity{display:block;}
</style>
Go to the block permissions and remove Guest from the view permission.
The block won't be visible to anyone and the activities visible only to authenticated users.
