Are the altimetry data adjusted to the Geoid, or only to the Ellipsoid?

The elevation data are relative to the ellipsoid.

The data also have a parameter indicating the geoid height, which is the height of the EGM2008 geoid above the TOPEX/Poseidon ellipsoid for the first and last shot in the record:

GLAH06 Data_40HZ/Geophysical/d_gdHt
GLAH12 Data_40HZ/Geophysical/d_gdHt
GLAH13 Data_40HZ/Geophysical/d_gdHt
GLAH14 Data_40HZ/Geophysical/d_gdHt
GLAH15 Data_40HZ/Geophysical/d_gdHt