Water absorbs infrared energy before it reaches the bottom of the pool, which constitutes about 52-55% of the Sun's radiant energy at Earth's surface. Visible light represents about 42 percent of the Sun's radiant energy, but as you stated water is almost completely transparent to visible light at normal pool depths. What happens next depends on the color of the walls and floor of the pool. A pure black surface would absorb all of the visible light, nearly doubling the amount of heat added to the pool. A purely reflective surface would reflect all light and add no appreciable heat to the pool. So if your pool's surfaces absorb even 25% of the visible light that strikes them, they're going to add an extra ~20% more heat to the pool than a white surface.
My pool's surface area is about 50 m2, which means it receives about 165 kWh of infrared radiation per day in the summer and another 126 kWh of visible light per day. If my pool's floor and walls absorbed 25% of that visible light it would be boosting total absorbed energy by 31.5 kWh, or 19%. It's enough to add an additional 0.5 - 0.6°F of warming per day.
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