Does the cloning software save the image as a file or as a mirror copy? If it saves it as a file, I don't see a problem with backing up your C drive to it, but if the image software makes a mirror copy, you could run into some issues.
Simple, look on the external hard drive and see if it looks just like the contents of your hard drive or if you have an image file that is roughly the size of the occupied space on your hard drive.
Correct, it would appear that it is doing a "disk-to-disk" image, instead of a "disk-to-file" image. So I wouldn't touch the contents of that drive for the image's integrity.