Not according to Australian Sports Comission statistics. They would argue that "Football (Outdoor)", which I can only assume is soccer seeings as "Australian Rules Football" is listed seperately consistantly maintains higher participation rates.
You can look at the statistics for 2009 at the following link (it will open a pdf of about 2mb):
http://www.ausport.gov.au/__data/assets/pdf_file/0005/377069/ERASS_Report_2009.pdf
And thats only if you compare to other football codes. If you're looking at all sports, as you said, it is outranked by a number of sports participation wise.
Suppose it depends on how you measure dominance.