That usually depends on the item, sometimes the manufacturer wants a receipt other times not. Corsair gave me a really hard time over some RAM, they ended up replacing it but didn't warranty the replacement set which I thought was odd. Any dealings I have had with AMD they go by the SN# of the CPU and have never asked for proof of purchase. That being said the last RMA I had with them was an FM2 CPU so it was a couple of years ago.
With the second-hand BNIB, I'd be more concerned about getting scammed and definitely wouldn't buy anything from Asia and the area.