This was actually the premise of
1214 from last year, but I don't think it was ever completed.
“1214 is a psychological horror video game where your own mobile phone is your worst enemy. With your phone being the indispensable requirement to enjoy this adventure, we can offer new forms of gaming never before seen thanks to the numerous possibilities that smartphones can offer. So that, the development of new puzzles using the vibration of the phone, strange calls… the possibilities are almost endless. Plus, although you aren’t playing on your PC, that doesn’t mean the game can’t keep playing with you.”
Using the latest AppGameKit V2, you CAN set local notifications which will display a notice on the user's phone at a specified time in the future.