Do electric water pumps actually add power?

Yes, mostly at higher rpm — single-digit to low-double-digit horsepower, not 20.

• Stock 6.0 on the engine dyno (Westech): a Gen III iron truck 6.0 with its truck accessory drive (water pump, a non-charging alternator, an idler in place of the power steering pump) vs a simple electric pump. Below about 3,200 rpm there was a slight loss on the untouched stock tune; above that the electric pump pulled ahead, reaching +11 hp at 5,800 rpm, the highest speed tested.
• 2012 Camaro on the chassis dyno: swapping the mechanical pump for a Meziere electric pump went from 385 to 391 rwhp (+6). Meziere says the pump draws roughly 12 amps (about 150–160 W), a negligible load.

Why: the water pump is the biggest power consumer on the accessory drive. Meziere's testing also found that stock mechanical pumps cavitate badly above about 6,500 rpm, which cuts flow, so the gap probably grows above the speeds tested.

The catch: for sustained high-speed driving the electric pump has to be a high-output unit to cool properly, and the good ones are expensive. If you keep a mechanical pump, OnAllCylinders reports Edelbrock test data showing its LS pump flowing about 17% more than the OE LS1 pump (roughly 58 → 68 gpm) while taking less power.