If this is clumping litter she is eating,it will form like cement inside her and yes,it will be fatal,I'm sure and you did ask if it would kill her.
I've had cats all my life and haver never heard of a cat eating litter,normally cats are quiet picky eaters.
If you want to find out if she is lacking anything,your best bet is a vet,she will most certainly die if she continues this strange behaviour.
"The cruelest animal is the Human animal"
3 kitties,Rocky(r.i.p my boy),Chico,Vinnie