In terms of energy, I would expect this to be equivalent to pumping the same volume of water up a mountain of the same height.
How strong does the sphere need to be? The air and water will be at roughly the same pressure, but air is less dense, so it at least needs to be strong and heavy enough to counteract the buoyant force.
Not quite the same thing. When you pump water up hill it comes all the way back down the hill, gaining speed as it falls, and then goes through a turbine. In this case, the water is being pumped out of the sphere against the pressure at that depth. When the water is let back in it only travels a short distance but at a high pressure due to the weight of the water above. So you see, the physical systems are actually quite different. In some ways this is more similar to compressing a spring.
If we assume that the mountain-tank is connected to a pipe of constant diameter, and that water has a constant density, then the speed at the top has to match the speed at the bottom.
If the water could not gain speed on the way down it would stand still at the top of the mountain. Put gravity into the equation and the water gains speed.
Thanks to pipes, the potential energy is not converted into speed on an open ramp along the slope of the mountain, it is converted from pressure to speed right at the turbine station. Any inertia within the pipes is just a medium for the pressure transfer, much like the inertia of a spinning axle in a mechanical transfer of torque. It is there, but it is not the driving force.
How strong does the sphere need to be? The air and water will be at roughly the same pressure, but air is less dense, so it at least needs to be strong and heavy enough to counteract the buoyant force.