So the animation will "wobble" and PositionTexture will show the motion of the sub.
Yup. Caustics are caused by the movement of surface waves, so you do see "animating pattern" even when nothing is moving - unless it's dead calm in which case there are no caustics either?
Free caustics generator (can do animated stuff too):
http://www.lysator.liu.se/~kand/caustics/