At least one author does describe it this way, but others state that "The Thomas precession comes into play for a gyroscope on the surface of the Earth ..., but not for a gyroscope in a freely moving satellite." An objection to the former interpretation is that the Thomas precession required has the wrong sign. The Fermi-Walker transport equation gives both the geodetic effect and Thomas precession and describes the transport of the spin 4-vector for accelerated motion in curved spacetime.
This viewpoint is supported by at least one author, but others claim that "The Thomas precession applies to a gyroscope on Earth's surface ..., whereas it does not apply to a satellite in free flight." A counterargument to this interpretation is that the required Thomas precession has an incorrect sign. The Fermi-Walker transport equation explains both effects and describes how the spin 4-vector is transported during accelerated motion in curved spacetime.