Yes, that's what one would think, but it appears something gets lost in translation with Immigration and there have been cases where your CTA gets 'cancelled' or 'revoked' unbeknownst to you until you operate a flight in and hold up the rest of your crew for an hour trying to get it sorted.
I'm just trying to get my ducks in a row here as I have a tight time frame between leaving Oz as a tourist and re-entering as crew. That being said, I did manage to get some info from some outfit that does visas here, now it's just up to the Immi when I get in not to stuff it up for me!