You can register a Nectar card (giving name/postal address/email address/phone number/date of birth), but I'm not sure how much verification of these things they do.
I am not sure, but I think you might need to register to redeem points.
There would be CCTV and maybe more if they used a payment card for the purchase. Whether Sainsburys would lift a finger to investigate a small loss is another matter.
I am not sure, but I think you might need to register to redeem points.