Of course it has. But you need to realize that even Gerber doesn't have advanced information you need for more complex designs (i.e PCB dozens of layers with different type of impedance, etc). For that you need an EDA with IPC-2581 support that even Eagle (AFAIK) doesn't have and many other commercial EDAs also don't.
Impedance has no connection to gerbers. You agree with manufacturer PCB type (thickens of prepag for each layer) and based on that you calculate thickness of line to meet certain impedance. It is totally designers responsibility.