not per se, rather they hold competitions called regionals every week during semester where you compete against the other unis, this year they were held at usyd, im not sure what they are doing next year, I only went for the first semester...
there is the debates and public issues committee of the uni of syd union which coordinates most of the stuff, at O-week there will be a stall for sure where you can sign on the mailing list for debates and public issues,
if your a debater there are a number of tournaments you can elect to try out for, there are the easters (national intervarsity championships) sydney takes the approach of using it as a tournament for our novices, then there are australasians and then worlds...