Wouldn't that adjustment depend on the actual image the adjustment is being made to? Each image would be slightly different. The Sync feature uses exactly the same adjustment on all images synced.
The "Auto button" from the "Lens Corrections Menu" works individually for each picture. When you press it, then Lightroom tries to find the Horizon and straightens the picture. When you press sync then the feature is applied to all the pictures but not correctly. If you go to the next synchronized picture the Auto button will appear pressed but the picture will not be straighten. If you reset the image and press the button manually then it would work just fine.
Right because when you use the Sync feature it makes all the same adjustments, rotation and cropping, as the original image is it syncing from.
This is not a setting that can be synced like exposure, sharpening and the like.
If you save a pre-set with lens corrections including auto align checked is the result different? If it operates like the lens corrections - distortions and chromatic it might/should depend on the data in the file not merely copying a setting as in Synch. I don't know the answer but it's worth trying