A forced-air system, whether mechanical-driven supercharger or turbo-supercharger, crams more air into an engine. Add more fuel and you get more power, so you will probably get less MPG. How much less will depend on how often you push the engine into boost. I have a turbo and if I drive gently-to-moderate I don't see much difference. When I'm in giddy-up mode, it's definitely worse. I'll let someone with a mechanically-driven supercharger chime in on their experience.
According to Bank's, the turbo produces more torque at 1,600 than the maximum a stock motor puts out. I have an '05 Rubicon 6-speed with stock 4.10 gears and 35's. I could only use overdrive on flat level ground. Now I don't have to downshift going up pretty much any hill. Forced induction really has made it more fun to drive. It's not a muscle car, but I no longer wish it had more power.
View attachment 139021