I don't believe that GE has any easy way of doing this. Maybe through the experimental/unsupported API? There is freely available, or at worst very inexpensive, DTED data out there that you could download and use a lookup from the KML lat/lon to the DTED terrain elevation. For example, search around through the links
here and you will find some after not too long. Still, not a good solution and it would be much easier if GE had a way to export terrain heights (if they're allowed to do this).
The problem is that when you export to KML, the GE Client doesn't write out the terrain value (as you already found out) and instead writes out 0 elevation and uses the default <altitudeMode> of clampedToGround (not specifying it in the KML gives it the default value) in order to display the path correctly.
This made sense to the people at Google because by using clampedToGround, the path stays on the ground and displays correctly whether the Terrain is turned on of off in the Layers.I