If the altitude of your image overlay is set to "clampToGround", then it should drape correctly over Google Earth's "Terrain" data, but any "3D Buildings" will still stick up through the image. If you need to visualize your elevation or other raster dataset, you can turn off the 3D Buildings layer, and you should get the draping you want over the Terrain.
A little background in case it's helpful...
Google Earth has two different 3D datasets. There's the "Terrain", which is the general 3D model of the Earth's surface, including mountains, valleys, etc., over which the satellite imagery is draped. The Terrain data varies in resolution and quality depending on data availability in different parts of the world. Then there is the "3D Buildings" dataset, which contains the detailed 3D models of buildings, trees, and in some places, a bit of the ground/terrain. That data only exists in select cities and towns around the world, the list of which is growing. In Google Earth Pro (v7.x, desktop app) you'll find the "Terrain" layer at the bottom of the layers list, while the 3D Buildings layer is in the middle of the Layers list, where you can turn them on and off independently. In the newer Google Earth (v9.x) for web and mobile, you can turn on/off the 3D Buildings data by going to menu > Map Style > "Turn on 3D Buildings", but there is currently no control to turn off the basic Terrain.