Getting air in and out of a small displacement engine efficiently is key in producing power. The smoother and more even the exhaust manifold, the faster and more efficiently the gases enter the turbo.
A header is still an exhaust manifold but usually less restrictive that the typical stock manifold made from cast iron. And yes you can have a header in a turbocharged car.
headers are just exaust manifolds made out of tubing , it would make a difference , in most any exhaust system the most power gains come from headers although they would be some pricey mofos for sure in our car