The serializable fields on SkeletonAnimation would be:
SkeletonDataAsset skeletonDataAsset;
string initialSkinName;
string animationName;
bool loop;
float timeScale;
bool initialFlipX, initialFlipY;
// all the flags and settings under "Advanced..."
// ...
What wouldn't be serialized are everything in the internal Skeleton and AnimationState since they live in the pure C# side (they aren't serializble UnityEngine.Objects)
Meaning the specific active animations at the their specific playback time, and the skeleton's specific pose, wouldn't be serialized.
It's not to say they can't be serialized since those can be stored as a crapton of floats and strings.
It's just that whole-GameObject serialization, I assume, wouldn't pick them up.