While the gravitational wave (though tiny) is radiating energy away from the earth - satellite system it is also changing the shape of the geodesic. The geodesic is a function of all gravitational effects. However, the satellite is also being decelerated, so the satellite will not follow its geodesic path exactly.
In the case of atmospheric drag, an additional force is acting on the satellite acting in opposition to its velocity and causing it to decelerate. In this case the satellite does not follow the geodesic as that path is only followed by an object in free fall, not an object undergoing acceleration.

In effect as in both cases there is acceleration and not free fall, neither is following a geodesic.

While the gravitational wave (though tiny) is radiating energy away from the earth - satellite system it is also changing the shape of the geodesic. The geodesic is a function of all gravitational effects. However, the satellite is also being decelerated, so the satellite will not follow its geodesic path exactly.
In the case of atmospheric drag, an additional force is acting on the satellite acting in opposition to its velocity and causing it to decelerate. In this case the satellite does not follow the geodesic as that path is only followed by an object in free fall, not an object undergoing acceleration.

In effect as in both cases there is acceleration and not free fall, neither is following a geodesic.

(Of course, Newtonian mechanics doesn't have gravitational waves. So for that reason the satellite, without atmospheric drag should continue to orbit, in free fall, for eternity.)