No it doesn't.
THAT quote / page doesn't state specifically that if the watch model has cellular, it doesn't additionally need a call plan attached to it to be able to call your HOME UK emergency services, regardless if an iPhone is nearby or not. It only states it might not work internationally.
For the paragraph that's near it says "In some countries and regions, international emergency calling works even if you haven't set up a mobile data plan on the watch. Find out which countries and regions are supported."
If you follow through the Find out... section and go to see what International emergency dialing shows for the UK under : https://www.apple.com/uk/watchos/feature-availability/#communications-international-emergency it says UK3 . The 3 sub category proviso states " Device must have been set up for mobile service with a network provider but does not require an active data plan. support.apple.com/en-gb/HT207578"
On that HT208578 page it states, under the Before You Start section, "Make sure that you have an eligible mobile data plan with a supported network provider. Your iPhone and Apple Watch must use the same network provider,* and you must be within your provider’s network when you set up cellular on your watch. *An Apple Watch that you set up for a family member can use a different network provider than your iPhone uses."
Even though I rang Apple directly and gave them a very specific scenario saying that if the cellular Apple watch would be used in the UK without a call plan, that following a fall, would it call the UK Emergency Services, the Genius said yes it would. On Apple's own support pages it says to make sure you have to an eligible mobile data plan.
So, if the Genius is to be trusted, it reads as..
1. If the Apple watch cellular owner lives in the UK on say Vodafone, doesn't need to make non emergency calls on the watch when their iPhone isn't near, as long as the watch is seen as a mobile device on their network, then they wouldn't need to transfer to EE or O2.
2. If the Apple watch cellular owner lives in the UK and wants to make non emergency calls on the watch when their iPhone isn't near, then they need suitable call plan for the watch that only EE or O2 can provide.
All of this infers that someone ALREADY knows if they pick up an iPhone or Apple watch with cellular (without nearby iPhone), which doesn't have an activated SIM / eSim, that you can make an emergency call.
