Yes. Pilots only need to have submitted an application for an AVID or an ASIC to operate an aircraft. The application will be processed and appropriate background checks undertaken prior to the AVID or ASIC being issued to an eligible pilot.
That meets CASA's requirement to fly as PIC of an aircraft. It does not satisfy the requirements of the Aviation Transport Security Act and Regs for an airport operator to allow unescorted access at a security controlled airport.
Geez CASA made a complete dogs breakfast of their issuing body program. They are the last ones who should be pedalling out advice on regulations for which they have no authority.
Just go flying. You still have an ASIC and as it does not state that it is expired, who can say that it is. Go on, read your ASIC, then tell me where exactly it states that it ever expires ...
Aviation Transport Security Regulations 2005
6.32 ASICs — period of issue and expiry
(1) Unless earlier cancelled, an ASIC expires at the end of the last
day of the month specified on it as its month of expiry.
Just because it doesn't have in big bold font "expiry" on the card, does not change the fact that if it is the first day of the next month and year after what is printed on the card. It is expired. No ifs, buts or maybes.