I haven't tried it. But it should work, as long as the wubi bootloader (don't know if it is just grub) is reinstalled. Replacing root.disk should do the trick.
root.disk is basically just a raw hard disk in a file.
You can see its partitions and block-size with:
fdisk -lu root.disk
you would get something like this:
From this you need to find the offset, at which point the ubuntu partition starts. In this example, the offset is 32002048 times 512 = 16385048576.
Sector size (logical/physical): 512 bytes / 512 bytes
I/O size (minimum/optimal): 512 bytes / 512 bytes
Disk identifier: 0xf0000000
Device Boot Start End Blocks Id System
/dev/sda1 * 2048 31999999 15998976 82 Linux swap / Solaris
/dev/sda2 32002046 976771071 472384513 5 Extended
/dev/sda5 32002048 976771071 472384512 83 Linux
Then you can mount the Linux/ext# partition with:
sudo mount -o loop,offset=16385048576 root.disk /mnt
Remember to switch the offset number with the correct number from your file.
So, I guess what I'm saying is backing up root.disk is sufficient to keep your files.