As it can be seen in this GIF :

When a KML polygon with holes is copied or transferred to My Drawings, the holes are deleted. The whole section <innerBoundaryIs></innerBoundaryIs> is deleted.
I then tried to replace the my_drawings.kmz of my workspace with a KMZ contaning polygons with holes. The holes were present. So ArcGIS Earth is able to correctly read the <innerBoundaryIs> tag. It is just not able to transfer it to My Drawings.
Thank you.