Yes you can do the survey if your policy is through superannuation. In your case you would select AIA from the list as they are your insurer. If you win the competition you would just need to provide a copy of your super member statement (with any sensitive information blanked out) as proof that you have this insurance through your fund.
It doesnt make it clear if you can do thesurvey if your insurance is through your Superannuation. Hestas is through AIA which is listed. Anyone know?