The web cam on the ship would not follow our every move, it would be focused on where we are sailing. The camera exists and can be viewed on the in-room TV. From it you can see the ocean and sometimes part of the prow of the ship.
Other ships have these Cam's connected to the internet and viewable from KROOZ CAM at http://www.kroooz-cams.com/
It is fun to see where the ships are. One time two ships were docked in Miami prow to prow. I could see each from the ship cam of the other.