You might be able to. When you go to your devices in your apple account to review warranty and such, you can put in your serial number to see if your eligible. I called and added it one for the last watch and apple send a signal to test the watch and run a diagnostic to make sure it is working.
They say you can't, but others have done so. I purchased a refurb iPad that everyone said I would not be able to get Apple Care and I went online and it sent a test to my device and allowed me to obtain Apple Care with no questions asked. It was not an Apple refurb, I got it from Amazon. It's worth a shot, worse thing is it will decline the purchase.
I bought a watch series 3 that was 5 months old and in pristine shape, took it to an Apple store and couldn’t. I also tried online and couldn’t. I then sold it and bought a new one series 4 and added it.