If I peeled potatoes & store them in cold water, will they absorb the water?

The potatoes are porous and so some water will be absorbed by the peeled potatoes over time. However, you didn't mention how long you plan to store them in water. Typical peeling one day and using the next day is fine. Restaurants often do this with cut potatoes for fries, so that excess starches on the outer surfaces will fall to the bottom of the container.