Sim, achei: eu coloco & & depois do meu último comando logo antes da declaração else:
...
# Backup using rsync
rsync --log-file=/home/fileserver/Applications/Backup/logs/rsync.log -avhP --delete /home/fileserver/Media/Books/ /home/fileserver/Backup4TB/Books >/dev/null 2>&1 &&
# SYNTAX ERROR IS HERE - If check is unsuccessfull
else
...
Ao remover o & &, o erro desaparece:
...
# Backup using rsync
rsync --log-file=/home/fileserver/Applications/Backup/logs/rsync.log -avhP --delete /home/fileserver/Media/Books/ /home/fileserver/Backup4TB/Books >/dev/null 2>&1
# SYNTAX ERROR IS HERE - If check is unsuccessfull
else
...