Depends on how much damage to the root has occurred. Sometimes they die, sometimes they don't, and sometimes they will branch and continue growing. The plants can also grow new roots. I don't worry about it too much if a root gets broken.
i hope it branches. It wasn't a clean break away, it sort of snapped on the outside and it's turned a little black at the break points. i'm concerned b/c i recently repotted in S/H, and at this point every healthy root counts.