I'm not sure if you have the right idea about backup images ...
A backup image of your C: drive is an exact copy of your C: drive, so since your C: drive is bootable, the image of your C: drive is also bootable.
You don't want to store that image on your computer; the whole idea of having a bootable backup image is that you can restore the image even if your computer is messed up beyond redemption in this world and the next - even if it's a smoldering pile of ashes. That's why image backup programs have you make what they call a recovery environment, which is really just a way to boot your computer (or its replacement) from the image.