The amount of tiny tubes you would need would be prohibitively expensive to produce and would generate tiny amounts of energy as the amount of water actually drawn up would be miniscule.
Per Wikipedia, following the relevant formula...
Thus for a 2 m (6.6 ft) diameter tube, the water would rise an unnoticeable 0.014 mm (0.00055 in). However, for a 2 cm (0.79 in) diameter tube, the water would rise 1.4 mm (0.055 in), and for a 0.2 mm (0.0079 in) diameter tube, the water would rise 140 mm (5.5 in).
So, assuming you could produce a tube 0.2mm in diameter, you could expect a column of water 14cm high. I don't know how quickly the water would rise, but I'm guessing pretty slowly, so you're looking at a tiny cross sectional area of water rising a tiny height. The mass of the water will be tiny, so the GPE that could be recovered by letting the water fall back to earth would also be tiny. You'd be lucky to overcome friction in the generator.
Build a hydroelectric dam.