Can you apply a GUISkin to an Editor GUI?

The short answer is "Yes"!

Gui.skin = EditorGUIUtility.Load("LevelEditor/LevelEditorSkin.guiskin") as GUISkin;

The untility allows you to load resources but they have to be inside a "Editor Default Resources" folder which isn't inside the Editor folder but in the project root. Then you don't refer to the "Editor Default Resources" in the path but the hierarchy below that. Also you have to include the file name and the file extension (which seems to go against convention) but then you assign the GUI.skin normally.

It works as you would expect it would in any other situation. Still the documentation is somewhat lacking.

I hope this helps.