Beside the alarms themself there is also an entry in alarm_queue.ini for HAM updater on every device and modest (email) refresh every x minutes (if this feature is used). Those two services need internet connection to work and they don't connect on their own, which is fine. What I'm not sure of is whether if those two things still get updated when the phone is connected again? In simple words: do you still see new updates if device wasn't connected at specific time? And what about email?