I doubt they'd send back a non-functioning watch. Having worked at an Apple Retail store for a few years, the policies stress the importance of repairing devices rather than replacing where possible to maintain the value of the product, and YOUR particular unit. If they swapped things out left and right, eventually we'd see them as disposable.
For those of us who got the "We're sending the product to you along with a letter that provides more information." email, you can track the package by reference on FedEx by using the Repair ID, your shipping zip code (use the store's zip if you opted to send it there), and today (11/5) as a ship date. It was sent priority overnight, so we'll get them back tomorrow. That is - for those of us in the USA.