Yes you can turbocharge a naturally aspirated engine however you need to do some modifications to the engine to make it turbocharged and that can be costly.
The naturally aspirated engine will require modifications to the compression ratio, ECU mapping, and fuel delivery for the turbocharger to work properly on the naturally aspirated engine.
So it's not as simple as just adding a turbocharger to the naturally aspirated engine but it can be done if you know how and have the money to turbocharge the naturally aspirated engine.
Your fuel mileage might drop as well and the engine when turbocharged will require more maintaining to keep it working properly.
Some videos and magazines for cars make it look like it's simple as installing a turbocharger on your naturally aspirated engine but it's not as simple as that and requires some knowledge on how to install it and change the fuel delivery, compression and your vehicles computer.