There are only two options Facebook allow to play in Newsfeed: a direct Youtube video or Vimeo video and a direct upload of an mp4 to FB's servers.
So the answer would be no, as much as we wanted to support this, Facebook won't allow us.
To share a video in FB or Twitter, users can share the page the video is embedded on, or you can use the public page we provide (which, by the way, is why we provide it).