Forced induction will burn more fuel since you're adding more air. Turbos have better milage than superchargers though since the engine isn't using energy to turn the blower. you can get good milage if you stay out of boost, but I can tell you it is a pain to keep the urges down.
One argument I heard, is that you don't have to mash the pedal as much on lower powered and heavier cars to get up to speed if you have a SC/TC, thus saving fuel, is that true?
No. You may not have to push the pedal down, but forced induction will not give you better mpg.
Here is how the forced induction thing works to make better mpg.
Say hypothetically you have a 2,000 lb car that you are going to power with a 2.2L N/A engine. You can get better mpg by using a 1.6L turbo motor instead of a 2.2, not because of the turbo, but because it's a 1.6L motor. Your fuel savings will come in at lower speeds when you are NOT using the turbo to make power, not "boosting" as they say.
Simply put you cannot get better mpg by adding a TC or SC to the same motor you already have. You have to remember the golden rule: Anything that makes more HP will NOT make more mpg.
Most people do not realize this. Even adding cold air intakes and ram air systems will not add mpg. They force more air into the engine, which makes the car add more fuel to maintain the proper air/fuel mix, meaning more fuel burned and less mpg.
If you want to add a turbo, but want to keep most of your mpg, you will have to modify your driving habits to get better mpg. The "All about mpg" section has a lot of good info for doing this.