A:Answer Great question. The device has WiFi in order to communicate with multiple platforms like your smartphone via app notifications. So, yes, in the event that your WiFi router is the source of the fire, then nothing relying on internet connections would work. This is simply an added layer of protection to notify you if you're not home. In addition, it has other feature like weekly tests and automatic sensor checks. It will still work without internet with an audible local alarm, you just wont get a notification on your smartphone. The National Fire Protection Association (NFPA) states that fire alarms should be installed at each level, inside and outside bedrooms. Lastly, the chances of the fire taking out the wireless router before Nest Protect can sense it are pretty slim, as long as you follow the NFPA recommendations.
Here's the NFPA guide to fire alarms: https://www.nfpa.org/Public-Education/By-topic/Smoke-alarms/Installing-and-maintaining-smoke-alarms
Here's a great article to learn more: https://www.howtogeek.com/362600/will-the-nest-protect-still-work-without-a-wi-fi-connection/