Not if the permissions are set correctly and you are using the latest version of 2.x, the only two places where you may get any hint of a private post is the last post title in the user profile (not sure if thats an issue still) or on the forumhome page if you have it set to show hidden forums that users can't access. If they appear via the search for members who don't have access then you've set the permissions wrong.
Remember that you'll see them in the search results because you have access to them