Modes 1 & 2 are seperate from the rest. They cannot be set by any other way than the advanced display settings. In these display settings, there's a box for geometry settings which allows you to select vertex, wireframe, solid, or texture.
But when you set the Geo Mode for all surfaces this way, the engine does not update each surfaces' mode. So the settings set by the advanced display options cannot be retrieved through Cog.
However, Geo Mode 3 shows that the Geometry settings in the advanced display options are Geo Modes even though they do not reset the surfaces' modes. Geo Mode 3 can be set and retrieved through Cog. But when it is set in the display options, mode 3 is not given to the surfaces. This proves that the Geo Modes set by the display options are not given to individual surfaces. So we can safely assume the modes 1 & 2 are Geo Modes that do have a purpose.
There are no Geo Modes greater than 4. For a while, there was popularly thought to be a Geo Mode 5 that had the same effect as mode 4, but that's because setting any mode greater than 4 has the same effect as mode 4.