Repairing an Apple Watch 3 with NFC?

Long time reader, but made a new account for posting. This is our first Christmas as a married couple. My wife has wanted an Apple Watch for years. It’s the perfect present.

We always set a budget for presents so it doesn’t become one-upping one another. A new Apple Watch is way over budget, but we buy used gifts for one another on occasion to make the budget (she bought me a PS4 last year this way).

I’m trawling eBay and can find lots of Apple Watch s3 within budget, and a few Apple Watch s4, all of which are broken and need repairing. Generally broken screens. I’ve read that on Apple watches the NFC chip for Apple Pay is in the screen, and thus replacing the screen can render NFC useless. Is this the case even with a factory reset? I don’t want to go to all this hassle, if one of the major useful features of the watch will be permanently disabled with the repair.