I don't see why not. It all depends on the engine though. For CryEngine, the water volumes automatically project caustics based on some settings you can tweak. For Unreal, you can create a light projector and have it project the animated caustics. You might even be able to place it as a decal in Unreal as well? Not sure on that one though, but with the material editor you can achieve it in a variety of ways. Light projection is probably the easiest.
In Unity you could do this as a light cookie(projection) or as an animated reflection probe. I don't know what kind of performance the latter would get you, but you look nice if blended well.
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