You'll boot the Windows 7 DVD Repair console or Repair CD, select "Recover Using an Image" and it will detect the Windows 7 backup image stored on the external. That is the only booting that is involved with backup, and that is only used if you backup a System image and need to reimage the HD with it.
While everything is included in the image, it is also best to copy your files over to the external using either the backup utility or, more efficiently, by dragging the Active User files to the external.
Then you'll have a Backup image which can be reimaged to the HD or a replacement in 20 minutes, or you have files to choose from in case you lose them or they are damaged, or the backup image doesn't work and you are forced to reinstall.
For files, I backup Downloads, Documents, Pictures, Videos, Music and Internet Explorer Favorites, which is a lot smaller on the disk than using the blunderbuss backup utility.