A turbocharged aircraft will get to 2000 ft quicker than the same non-turbocharged aircraft because the turbo will be giving more than sea level pressure well above 2000 ft!
In practise is makes little difference from a sea level airport.
Having flown the non-turbo Arrow and the turbo Arrow, and the Seneca 1 non-turbo and II turbo from the same sea level airport.
The turbo aircraft will start to show the real benafits above 5000-6000 ft
JL.