I always assumed that would be way too slow for most games. The water in Dark Cloud PS2 for example simulates refraction. I always assumed it was done by drawing parts of the previous screen or by drawing the screen once and then drawing the water over it and using the screen as the texture. Or by drawing parts of the previous screen. The same way the wake of the warpball in CTR did it's think. I guess you could call that Rendering to Texture but it doesn't require extra memory and it would work for lots of stuff. The only issue being if stuff got infront of the water before the water surface was rendered
In Hydro Thunder, there was another technique for reflection and refraction. In some parts of the level the water "reflected" by actually drawing the terrain above the water upside down and there was a wiggle applied to the upside down verticies to simulate the undulating effect that moving water would have on the reflection. In other parts of the level the water "refracted" by drawing the underwater geometry and I don't remember if the verticie wiggle was done for this geometry.
This is the non-render-to-texture way to do it, but can look damn good. If the verticie wiggle is done taking in to account water height I suppose it gets even better. And if the verticie wiggle is done taking in to account eye position and water height then it will be a hefty calculation but maybe doable on a PS2.