If the header of my KML file says it is 2.0 or 2.1, will it still display in ArcGlobe?
Yes, based on the object-level support detailed above. Supported KML objects will be displayed, and unsupported KML objects will not. The KML 2.2 specification is a modified extension of the KML 2.0 and 2.1 specifications and shares many of the same elements. It is possible to have a KML 2.2 file that contains only tags defined in an earlier release of the KML specification.