I believe they can do it. They can also do it over the phone in advance. I think that they now charge for the service and is more expensive than just going to the online site
Personally, I wouldn't recommend waiting until you get to the airport in case it issues you a referral number rather than an ETA. I have seen a referral be issued once before which involved contacting Australian High Commission during normal business opening hours to get it agreed. Not something I'd want to risk at the airport
Dave