Blog Directory 1.1.8 currently requires a blog with Multisite Privacy of "Allow search engines to index this site." in order to be visible at all in the directory, even if the user is logged in.
This is how I see it...
#1 User is visitor (not logged in): Multisite Privacy of "Ask search engines not to index this site" or higher
#2 User is logged in: Multisite Privacy of "Visitors must have a login - anyone that is a registered user of Beginning of Wisdom can gain access." or higher
#3 User is logged in and registered to the site: Multisite Privacy of "Only registered users of this blogs can have access - anyone found under Users > All Users can have access." or higher.
$4 User is admin of the site: Multisite Privacy of "Only administrators can visit - good for testing purposes before making it live." or higher.
I think that #1 and #2 are obvious needs for enhancement, and no, #1 is not fully implemented because if the site is hidden from search engines, it currently gets hidden from the directory. #3 and #4 are lower priority, because if the user is registered to, or an admin of, the site, then they should already be familiar with where the site is and go directly there without a directory.
This compatibility opportunity likely also exists with Recent Posts and related plugins, but I have not tested.