Turbo setups range from mild to wild. A basic setup will probably add 100 HP, and a full twin-turbo race setup might add 300-400.
In theory since turbos are a demand-based power adder, a turbo engine that is gently driven will get about the same mileage as the same engine NA. In reality, any aftermarket or home-cooked turbo on the 3.8 won't be optimized by the factory, so it will probably use more gas. If you actually use all that extra power that you paid for, your mileage will plummet! Keep in mind that turbo setups almost always require premium fuel for detonation control, so there's some additional cost to think about....