To my knowledge none of the Nest stuff can be accessed by emergency services. I'm very happy with that given that the Police are one of the services. I would remove these cameras from my home if I thought they could access things, and instead just build my own system that they couldn't access.
I wonder if that can link up with 911eye (999eye in the UK) https://www.capita.com/our-work/saving-lives-live-streaming