I assume your question refers to working in a disconnected mode (without ArcGIS Server in the picture)? Since the GeometryService needs a LocalServer to run upon, and spinning up the LocalServer requires a Standard license - you will be needing the Standard license. If, on the other hand, your GeometryService runs on the Server, then you only need Basic in order to work with it.
I assume your question refers to working in a disconnected mode (without ArcGIS Server in the picture)? Since the GeometryService needs a LocalServer to run upon, and spinning up the LocalServer requires a Standard license - you will be needing the Standard license. If, on the other hand, your GeometryService runs on the Server, then you only need Basic in order to work with it.