The quick answer is yes, the long answer is that if the buddypress User’s role is set to something greater than Subscriber, for example it is set to Author, and the Facebook plugin is installed and the Facebook plugin has been configured with a Facebook Application ID, and the facebook application has been configured properly, and the buddypress user has opted to link their facebook account with their buddypress accound then when the buddypress user logs into wordpress and writes a new post, they see a “Facebook Status on your Timeline” box below, containing a “Post to Facebook Timeline” checkbox, checked ON by default and the words: “This message will show as part of the story on your Facebook Timeline.”
If the above is in place and no errors are encountered, then when the buddypress user posts their post, the new post is automatically shared to the author’s Facebook Timeline(facebook wall).