Apart from shock mounting issues, there it the matter of drive spindle bearings. If you rotate the drive when spun up in any plane other than the one paralell to platters (i.e. perpendicular to drive axis), the bearing will be loaded laterally, for which it was not designed, theoretically shortening the drive's life. As tha car mostly rotates in horizontal plane (hopefully), the drive will feel best if it itself is horizontal.

However, I don't recall anybody reporting a drive failure that could be attributed to this.