As the Mopidy documentation states, the HTTP extension exposes the Core API. The Core API has no single method to do what you want. You’ll need to send two POST requests: one to add the station/song to the tracklist and then another request to start playback. If really you want to do what you describe then you’ll need to make your own simple web extension.
For the record: We’ve talked about making core.playback.play(uri) work without first having to add the track to the playlist. This will be probably be a reality in Mopidy 2.0 at the latest.