Sort of. Amazon sends the book to your default device that you specified. Then the covers are sent to the other kindle devices; and must be selected for reading on the other kindles before it is downloaded. A check-mark on the cover indicates that the book has been downloaded.
This was pointed to me long ago & applies to library books as well for the purchased books; it is a 'convenience' or liability depending on one's circumstances. My default is on my pc & it is a convenience to have the book on the kindle or fire hdx as that is where I read the books in kindle format or epub as was mostly the case.
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