Adding a Turbo to your engine will usually not improve your gas mileage although adding a Turbo to your engine will give your engine more horsepower out of a smaller engine.
When I added a Turbo to my engine my gas mileage actually dropped by 5 miles per gallon although I had more horsepower.
I actually removed the Turbocharger from my engine after I saw that drop in gas mileage even though I loved the extra horsepower from the engine.
I just could not afford to drive the car much after using so much more gasoline when the Turbocharger was put on.
So I removed the Turbocharger and sold it and actually made a bit of profit from it on ebay.
So Turbochargers can be great and improve your engines horsepower but you will usually see an increase in fuel consumption.