If you rsync a directory where an image might reside, it mirrors that directory but does it include boot ability?
What you rsynced was a directory, not the boot sector.
If you archive the file or directory, with tar, does it preserve its bootable qualities?
What you archived was again a file or directory.
Although this is not a problem, for the sake of the question I'll try to give a brief helpful answer.
The filesystem consists of booting blocks and then followed by the data blocks (commonly referred to as volumes). For security purpose basic file handling commands you mention above, rsync and tar, are aimed mainly at the latter blocks, the volume, where all data of files and directories are stored. Thus, consequently only these aspect of the filesystem is handled and done accordingly at command success.
To copy both, the booting blocks and data blocks you need to handle the two block sectors separately if you must need use rsync or tar. E.g. use "dd" to handle the bootsectors
dd if=/dev/<yourdevice> of=mybootblocks bs=1024 count=1
keep this file into a separate device or filesystem for safety. Then you can rsync the rest of the volume blocks, all files and directories for safe keeping too.
To restore the files unto the same device, in case of crisis:
dd if=mybootblocks of=/dev/<mydevice-in-SOS>
then next step is to rsync or untar the saved files and directories (data) to where they came from. Done.
That is for the method of backing the boot sectors coupled with rsync/tar on the data side. But the shortest way to back up the whole device is by simple use of "dd"
dd if=/dev/<mydevice> of=mydeviceasofDecember.img bs=2048
To restore is by simple "dd" by inverting the items.
Hope that helps.
Good luck and enjoy.