Would it be possible to install a turbocharger and supercharger in my 1997 mustang gt 4.6 ?
Yes, you can add a supercharger or a turbo kit to your 4.6 mustang. Obviously, you can't run both a turbo and a supercharger(at least without some major custom work $$).
Between the two- a supercharger would be better suited to your car. The rule of thumb is that superchargers are better for large displacement muscle cars, whereas turbos are more typically put on higher reeving, small displacement engines.
As the others have said, you can reuse your exhaust, but the intake will be replaced by the kit. If you have headers- those would need to be replaced, if you go with a turbocharger(unless its a rear mount kit).
Procharger and Vortech make several kits for the 4.6L 2V Mustang. The Vortech kit is less expensive than Procharger and they are both nice kits. I favor Procharger, but to each his own.
A top of the line bolt-on supercharger can increase your engines power to around 400 engine horsepower(350 to the wheels).