Yes, this can easily be done … when adding a “Home Phone” change the Visibility to either Private or Unlisted. This can also be done with addresses, email, links, dates and social media.
Private means the info can be seen by a logged in user if they have been assigned the View Private capability as set on the Connections : Roles admin page. SAme for Unlisted, except, by default, only the admin can view.
Hope that helps!