Technically yes. But there just isn't enough potential energy in the water falling on a typical house. For example, US average yearly rainfall of 76cm, on a 10

Technically yes. But there just isn't enough potential energy in the water falling on a typical house. For example, US average yearly rainfall of 76cm, on a 10m*15m roof, at height of two stories at 5 meters, would give you 1.5kWh of energy per year. That's enough to run the appliances in your home for an hour. You might be in a more rainy location, or have a larger home, but the end result is still insignificantly small.