Chris Cornell has an awesome voice, idk first thing that comes to mind when you say "rasp".
In any case, I know that it can affect your singing mildly for the next few hours and even into the next day. Not like a christian bale/batman difference but enough for her to care. My girlfriend is an opera singer and won't smoke the day of or the day before she has to sing because it affects her voice just slightly.
"From zero to hookah, in nothing flat."