Since you are planning on opening up the pc anyways, then don't do the backup to an external drive. Just install the second drive, and use a drive imaging program such as norton ghost, as an example. The imaging software will image one drive to the other completely with boot sector information and all. Then remove the original drive and put the second drive in it's place and boot up.
If you use the windows backup program to backup to an external drive then put that drive in the pc, it won't boot, won't work. You'd have to install windows onto a third drive and use the windows backup software to copy the backup over to the newly windows loaded drive.