From what I've seen it actually wouldn't change the rotation speed that much. Despite comparisons to Three Gorges and media calling it a "mega-dam" its design is completely different from a single giant dam with a massive reservoir.
The Yarlung Tsangpo Grand Canyon has a large bend and by digging tunnels through the mountains, water can shortcut a 2.2 km altitude drop in just 45 km, which gives it enormous amounts of kinetic energy which gets captured by five "dams" inside the tunnel. The mountains then function as a natural reservoir dam, so very little water gets lifted up, which is how the Three Gorges Dam slowed the Earth's rotation with its massive reservoir.


