Is it possible to add a gib to something (in this case a bloody head to the gibs for the regular head) and have it stay attached to whatever the thing it gibbed from was attached to?

The idea is to make a soldier's head turn bloody after it has been shot at enough to break, instead of having it explode.

why not just have the "normal" face attachable on the "bloody" head?

You mean over it? Like a mask? That might work as long as they don't shift too much.

They shouldn't, since CC joints are more welds than joints.

somebody did this with one of the clones once, "Clone of Fortune" or sth like that, it seemed to work pretty well

If you look closely at my melee actors in MMA, their faces are bloodied under their helmets. Same with their bodies, but the body armor doesn't come off that often.