By the way, I would recommend you have the serial number re-stamped.
Here is why as I have a story on this...
My fingers got fat, so I had my engagement ring resized at Tiffany. When it came back, the stamp was very faint. I could still read it, and told myself it's not a big deal, I'll live with it. I wore it for a few weeks and said "no, it is a big deal, I need that original stamp". I contacted Tiffany and asked the to re-stamp which they did, free of charge. That made me realize to be sure and check stamps on well-worn pieces and get them re-stamped. With luxury brand pieces that have a serial numbers, to me, this is the most critical item.
My point is I would recommend you re-stamp your piece while the serial number is still visible to avoid any authentication issues further down the road. For VCA, not having a serial number, even if it's because it is worn/rubbed-off is a big deal, and with your piece not having a COA, once your serial number fades further and can no longer be read, it may get complicated.
For me, I would do it for peace of mind. Just my two cents. Hope that helps.