You get a rise in a capillary tube because it reduces the energy stored in the surface tension at the air-water and air-glass interface. The water rises until the reduction in the surface tension energy is balanced by the increase in the gravitational potential energy of the water.
But it's not at all obvious how you could extract energy from this. If you evaporate water from the top of the tube then you will certainly pull up more water to replace the water lost by evaporation. I suppose this is analogous to a tree pulling up water, though my limited memory of biology I think the sap is driven up the tree by osmotic pressure in the roots as well as by capillary action. I suppose you could put a microturbine at the bottom of the capillary tube then heat the top and extract energy as the water rises up the tube to replace the water that's evaporated. However I doubt this would be as efficient as just using the same amount of heat in steam engine.
Were you wondering if there was a way to make the water rise up the tube, then fall back, then rise up again, generating energy with each cycle? The only way you could do this was if there was some way to change the air-water or air-glass surface tension in some reversible way. You can easily reduce the air-water surface tension by adding surfactant, and this will make the water drop, but you'd need to get the surfactant back out to make the water rise again.