That would only be the case if memories had an actual physical correlation to water. You could think of water as being one massive "Harddrive" that stores memories, but then again the stone is said to provide an endless source of water, and since it said water comes from memories then you're right, there would just be more and more water piling up until it becomes Water World up in here where the Throat of the World's summit turns into a tropical island.
It actually hurts a little to think about this. I can't figure out for sure, too many if's, and's, or but's.