An ECU is a tuning tool. It allows the tuner to alter the air-fuel ratio and ignition timing. So the whole point is that the ECU allows the tuner to affect the fuel economy!
Normally what happens is that some modifications that you perform to the engine will throw the factory ECU out of tune (for example, fitting larger injectors or changing camshafts); therefore putting on an aftermarket ECU allows you to bring the air-fuel ratio back to where it should be. Therefore on a standard engine, there’s no reason you can’t get the same fuel economy as a factory car, or possibly slightly better.
In practice, other modifications that you do such as higher overlap camshafts will increase the fuel consumption.