Hi DylanA,
Yes, police officers have the same powers under the law off duty as they do on duty. You can request their badge number and call the State Police Force they belong to, in order to verify their identity as a cop if you wish.
This is the Oath taken by Police officers in NSW:
I,, do swear that I will well and truly serve our Sovereign Lady the Queen as a police officer without favour or affection, malice or ill-will until I am legally discharged, that I will cause Her Majesty’s peace to be kept and preserved, and that I will prevent to the best of my power all offences against that peace, and that while I continue to be a police officer I will to the best of my skill and knowledge discharge all my duties faithfully according to law. So help me God.
You will note that it does not specify serving, only during periods they are rostered on.
In addition Police Powers and Responsibilities Regs in NSW provide as follows:
8 Performance of duties by police officers
...In particular, a police officer is required:
(a) to serve wherever the officer is duly directed, and
(b) to perform such police duty as may be duly directed, whether or not during the officer’s rostered hours of duty.
9 Responsibilities of off-duty police officers
(1) A police officer who is off-duty (whether rostered off-duty, on annual leave, suspended or otherwise absent)...is subject to the provisions of this Regulation and the Police Code of Conduct.