Yes, but the city was too long and thin to effectively demonstrate the power of the A-bombs. Some of the bomb's power was wasted on empty countryside. Plus the city is divided by a ridge that helps shield one part of the city from an explosion over the other part. The Targeting Committee protested the late orders to include Nagasaki on the target list, but they were overruled. Flattening Kokura Arsenal would have been a much more dramatic example of the power of the A-bombs.
Unfortunately we conducted a large conventional raid at Yawata just a few miles upwind of Kokura Arsenal the day before the second A-bomb mission, and the smoke from this raid prevented our bomber from getting a visual fix on Kokura Arsenal.
Additionally, Bockscar had a bad fuel pump that prevented the plane from using a lot of its fuel (but it still had to carry the weight of this fuel). Instead of taking the time to fix the pump or change to a different plane, we decided to launch the mission with a crippled plane. This gave the crew very little time to linger over Japan before running out of fuel.
Had we not made these two errors, it is likely that Kokura Arsenal would have been flattened, and the results of the second A-bomb would have been much more dramatic and shocking to the Japanese government.
Another error was not reserving Yokohama for the A-bombs. In addition to its industrial area being much more geometrically suited for a circular blast area, as it is a suburb of Tokyo the mushroom cloud would have been visible from the Imperial Palace. Yokohama should have been the alternate and not Nagasaki.