Would be great. But...
Not possible, at least not currently.
- device is single tasking, the OS is not running whilst your game is running
- the system menu is a limited exception, I'm not sure exactly how that's hooked up but I believe it's injected into your game
- system goes into hibernation low power state when sleeping
- use of Bluetooth or WiFi isn't allowed
- there would need to be 1M times as many Playdate in the wild to make it work
There was a phone game that did this with the scenario of a virus that slowly affects all people/phones. Can't remember the name.
I pitched something like StreetPass for iPhone back in 2014 but the funding body decided it wouldn't be popular enough.
The beauty of StreetPass is that the core functionality was built-in to the system.