Need for connecting with smartphone in emergency situation

While I understand that the smartphone is required to compose and read sms messges, but what about in the case of emergency, when I just want to send out a SOS message to the authority, so they would received my SOS with my GPS location, just like the SPOT Tracker does, would I still need to pair up the smartphone for this purpose?

The reason I ask is, in some cases of emergency, the simplest thing to do is to just reach for the inReach, and press that emergency button, the smartphone may not even be reachable, or working at that point.