Perhaps...if there was a convenient station close by. I find that the public bus going to the domestic airport is quite good though, and surprisingly not too expensive. Once you're at the domestic airport, a free shuttle bus transports travellers on to the international terminal. It's definitely not as fast as a train, but it's not too bad.
Yes, it's great! Bus 37 begins at Kings Park and goes through several suburbs to Belmont, and then on to the domestic airport. I'm in Bayswater so I can get the bus to Belmont, change buses at the Forum and get there that way.