Thanks for the feedback. I love how supportive you guys all are.
That said, no, I have not yet tried to do anything with caustics on this site. I have done a bit with it doing ray tracing, but for a video game, you probably need something faster than ray tracing.
While there is nothing on this site (yet) that can help you with this, there is no doubt in my mind that this would be possible to do with the right geometry and shaders. Just remember that everything in computer graphics is cheating, or some sort of shortcut, designed to make a nice looking environment, without having to completely simulate the physics (lighting, reflection, refraction, etc.), because that is usually way to slow.
The fact that I haven't ever tried this before aside, here's my first thoughts on how you might be able to piece this together. There are several aspects of this picture that make it work: (1) It fades out in the distance, (2) There's a glow on the underside of the waves that comes from the sunlight refracting through, (3) there are rays of light filtering through the water, and (4) the actual caustics on the ocean floor.
Here would be my first attempt at this. The terrain would be done using either a normal model, or possibly using some sort of algorithm to generate terrain, and then do my own custom drawing of the geometric primitives. There are tutorials here for that.
In addition to the ocean floor's base texture, I'd also add in some sort of Perlin noise texture (or a couple of them) and have them move around over time. That should give you the caustics you want.
You'll also need to add in something like fog, based on depth into the scene, but what might work better is some sort of distance based gaussian blur. There are a few tutorials around that I've seen for blurring, and I'd imagine that there might be something for depth of field blurring as well. Something in that mix will probably get you the desired result.
Additionally, you will probably want to add in some more geometry for the light rays filtering through the water. I'd look up tutorials for God rays, which will probably look about the same.
The bright sunlight refracting through the surface should be very similar to what you see in the reflection tutorial, combined with some sort of moving bump map or height map. You may have to change the math a bit to make it feel like refraction instead of reflection, though.
Wow, now that I've said all that, it sounds kind of complicated. There may be a simpler way to do it, and if you or anyone else has a simpler approach, I'd love to hear it. Like I said, that's just my first thoughts about the problem.
As I said earlier, there's no doubt in my mind that there's a way to make this work (good enough to fool the players), its just a matter of figuring out how. Hopefully that at least gives you a few more ideas to think about. Let us all know if you come up with something!