No.

A National Police Check done in the last 12 months is the ultimate check we need.  This is no substitute for a National Police Check because some certificates have an expiry date 5 years from now and not all IDs have websites to cross check the certificate's validity or currency.  Some of these organisations also don't ask you to hand in your certificate, even after you've left.

Teacher Registration (depending on the State) is generally renewed every 5 years and is valid for the State only.  So you can still hold a Registered Teacher Certificate and yet have multiple dangerous driving offences, drug offences, theft convictions, lying to police you will only be struck off the State Teacher's register if your crimes happen to be reported or self-reported to the Teachers Registration Board of your State.  As part of conditions of your Teachers registration you are required to update them at any time down the track of any convictions (but if the information is not volunteered, they will not necessarily check).

This is why we ask for a National Police check.