In a word: no.
The insurance company sees it this way: should it be determined that an Individual was not registered but was a paid member of the Association and held Public and Products Liability (Members) insurance, the insurance company would not consider the Insurance policy to be in place for any incident that produced a claim on that policy.
There's a simple reason for this. By law in NSW, any person who keeps bees and/or works with bees must be registered with the NSW Department of Primary Industries.
The insurance company would require all members who keep bees or work with bees to comply with the registration requirements of their local State Government.
It's the case that the ABA specifies that only registered beekeepers can obtain personal beekeeping insurance. However it has no way of preventing an unregistered member from applying online for insurance since it cannot validate DPI licence codes in real time.
So if you are not registered, you could try to take out and pay for a policy. But you'd not only be breaking the law, you'd be wasting your money: if someone made a claim against you, the insurer would regard the policy invalid.
Another reason to ensure you are up to date with paying your DPI registration.
We put members questions about their insurance to Irecon, the ABA insurance broker. For individual advice you should refer to policy details.