Sim, no T1 (Terminal Internacional) e T2 (Terminal Doméstico).
Eu estava lá em 2011, mas não me lembro dos detalhes (exceto que eu fiz usei conexão com a internet no aeroporto). Enfim, Foursquare é uma boa ajuda na memória, e várias dicas de 2011 e 2012 dizem que há de fato wifi disponível.
Free wifi all over with the "FREE WIFI BY EXPEDIA SYD" network. Just choose a destination and flight number.
You get free and fast wifi here!
Free wifi in the international terminal (T1)
Aquí el wifi gratis funciona!!!
Atualizar : o Site do aeroporto de Sydney também confirma isso:
Free Wi-Fi is available throughout International Terminal (T1) and Domestic Terminal (T2).
Sydney Airport now provides free Wi-Fi for all travellers at both the Domestic (T2) and International (T1) Terminals. You can use any Wi-Fi enabled device to connect including your laptop, smartphone or tablet.
Simply select “Free Internet by sponsors name & SYD” from the list of available networks, answer the questions, read the terms and conditions and click "Proceed". You will be shown a sponsored message then directed to a website.
From there you can browse the internet for up to 2 hours and 500MB of data.
Coverage is provided throughout the entire International Terminal (T1) and Domestic Terminal (T2).