Now that is a hell of a question.
I have shot and still shoot a ton of frangible ammo. I can't say enough good things about it. I think it is one of the best SD rounds out there. I have seen it tested a ton of different ways, but never on water. I would tend to think it would break up. It breaks up if you try to skip it off of steel. I think if there was enough force on the bullet to change it's direction then there would be enough force to break the bullet up when it hit the water.
It would also depend on the manufacturer and hardness of the bullet. You can use the same material in a bullet and make it so that it starts to break apart just by hitting drywall or if you "bake" it a little longer, get the same bullet, same material, to shoot through steel.