It's sorta the reverse of that. A turbo is just a compressor that allows more air to pushed into the cylinder than would be normally aspirated (breathed in) during the intake stroke. More air means more oxygen, more oxygen allows more fuel to burn and thus more power. Under load this will use more fuel than a same displacement normally aspirated engine, all else being equal. What the turbo does is let you use higher compression to get the effective power of a larger displacement normally aspirated engine. There might be some fuel savings for a turbo 4-cyl vs a V-8 with similar peak output though even then specific use conditions (towing, leadfoot driving, big hill climbs) will cause some variance in that comparison. The savings come when you are driving carefully and not spooling up the turbo. The ECU can sense this and will send less fuel to the cylinder when the extra air isn't there.I am not an engineer, so my understanding maybe faulty, but it is my understanding that turbos in general have little to no effect in terms of fuel consumption.
Turbos run off the exhaust gases of the engine and as such do not take any engine power to run them, so they do not make the engine to work harder.
About the only drain on the engine is that they do create some back pressure, but in general that one draw back does not effect fuel consumption and generally turbos are considered to allow an engine to create more power without consuming more fuel.
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