If it is an LTE model, I think the carrier could blacklist the IMEI, which would flag it should someone try to using it with LTE connectivity. However, I don't know if that would prevent someone just using it with Bluetooth or Wi-Fi connection. Check with your carrier.
I would think so. If the watch can be used like a phone and you get a bill from your carrier for data used. Or if you can make phone calls with it. At any rate, any proof of your watch being yours (sales receipt, imei number, etc.) would help you claim the watch when it's found. Good luck!! 🙂