It should but in your command composition, rsync will pick up other directories under /home/.
Although on the restore command these options (--delete --exclude={"/home/bmike1/.cache","/home/bmike1/.local/share/Trash"} ) do not make sense to me. A
Also, why do you need 'sudo'?
For my backups, I run the rsync commands directly from the user's home directory e.g. /home/bmike1/
FWIW please read the man page for -a and -A/-X nuances + logging the backup to record what went right/wrong.
(Note the changes in bold. Also, -a will not work for backup media (USB drives) formatted with Microsoft files systems (vfat, exFAT, NTFS)