No, it will not back up all of your GRUB installation.
If /dev/sda1 includes /boot/grub then it will backup the configuration and stage 2 boot files. It will not backup the part of GRUB that sits in the first 446 bytes of the
Master Boot Record (MBR) (stage 1) and will almost certainly not backup stage 1.5 that very probably sits in ~30 kB following the MBR.
Backing up and restoring GRUB stage 1 from the MBR using dd is described
here in the "Boot-loader or IPL (Stage 1) Backup and Restore" section but it's not much use unless you can also backup and restore stage 1.5 and netsearching did not find anything about that.
A better solution might be to make a backup GRUB floppy, CD, DVD or USB memory stick. Instructions for doing so are given on the link above. That way you could restore your partitions using a bootable Linux CD or DVD such as Knoppix and then boot from them using the GRUB floppy, CD, DVD or USB memory stick followed by re-installing GRUB.
This is not an area in which I have much expertise so hopefully someone with more knowledge will reply to this thread with more complete information.