Yep! The duplicated mesh will have the same UV layout as the mesh it was duplicated from. Then it becomes a matter of moving the UV's around in the UV texture editor so that you don't have the meshes overlapping. The good news is that small tweaks to the new mesh will update its UV layout. So using split polygon tool and insert edgeloop will automatically update the UV layout. BUT you have to be careful with extrusions because it wont automatically flatten out the extrusion so you can see all sides of the new extrusion in the UV texture editor.

Hope this makes sense