Is GCS_Assumed_Geographic_1 a coordinate system?

Answer

No, CGS_ASSUMED_GEOGRAPHIC_1 is not a real coordinate system. If the spatial reference for a data layer displays this name in ArcGIS Desktop, it means that there is no projection file associated with the data. To overlay the data correctly in ArcMap, take steps to define the coordinate system.

Warning:
Some data in later versions may have a projection actually defined with this default coordinate system. This definition is incorrect in all cases, and data with this definition does not align correctly with other data in ArcMap.

The 'GCS_ASSUMED_GEOGRAPHIC_1' spatial reference definition was created for earlier versions of ArcGIS to permit ArcMap to 'guess' at the coordinate system for data, which has coordinates in decimal degrees. This causes ArcMap to make the same assumptions about the spatial reference for data that exist in ArcInfo Workstation and ArcView 3.x.

To identify and define the projection for the data, see the link in the Related Information section below for more information in 'Projection Basics: What the GIS professional needs to know' and 'What geographic goordinate system or datum should be used for my data?'.