So, from the above, it seems you do not need to declare any offence in your ASIC application. For ten years I admitted to a civil offence, which was using a radar detector on a motorcycle. Issue of ASIC was never denied.
That seems rather odd. AUSCHECK informs the issuing body if the applicant has an adverse criminal record. Not the other way around. I have not heard of any application that requires you to declare criminal records.