According to a post on Reddit, it appears that the Apple Watch Series 3 with LTE may be capable of making calls to emergency services even without an activated cellular service, albeit rather slowly.
Series 3 RSS
iOS 11 recently leaked online and the new Watch app appears to show off the new Series 3 Apple Watch. It looks as though it will ship with cellular connectivity so you can de-tether it from a phone.
Apple will unveil a new Watch wearable at its September iPhone event. The new device will feature LTE connectivity and be able to make calls and stream music independent of an iPhone connection.