Whoops, sorry, thats not what I meant. I mean that you can't drop her sword, you can still use whatever weapon you want, you just can't drop the sword out of your inventory.
I kill her every time I play this game and I've never noticed a difference. lol
Usually when you kill super important people they just go unconscious and then wake up a bit later.
I'm not really sure what quest she is for, probably some vague side one. I've never encountered it anyways.