Currently, only published posts are returned from the Facebook Pages Connector. That is, it's using the /published_posts endpoint.
For Pages that advertise, this leaves out a large number of posts - the Ads Posts, which are available at the /ads_posts endpoint. Note that this endpoint also enables the retrieval of "dark posts", using the include_inline_create flag.
Not including these posts rendered the connector useless for us, as it does not actually provide an accurate picture of our Page's posts.