No. In order to retrieve information about the user (like user_id, email, etc.), they must authenticate with your app.
Keep in mind that although it works in the same manner, you can have users "log in" to your app with their facebook account, but not post anything, nor request any special permissions, etc. Kind of a change in perspective there. Make the default privacy on your app for each user "only me", and then it definitely won't show up anywhere.