If a chariot dies, does the character die also?
In the character mounts section, the rules say:


  A chariot mount follows all the rules for ridden monsters, save for the fact that a chariot does not need to take a monster Reaction test if the character is slain. (pg 105)


As such, if the Corpse Cart were to die, the Necromancer in question would proceed on foot, as he would have if he were on a Ridden Monster which died.