Say, I want to make an alarm clock app on android as a progressive web app.
Like a native alarm app, it should be notified at selected time even without active web page.
At first, I considered using push api. But of course push message cannot be arrived while offline. And also push message arrival time cannot be accurate enough for alarm clock.
Is it possible to be notified at the time even without network connection?
What you're describing is functionality that's more closely tied to periodic background sync, rather than push notifications, in that push notifications require a network connection. Periodic background sync has the advantage of being network-independent. (Periodic background sync is just a proposal right now, and hasn't been implemented in any browsers.)
But, unfortunately for your use case, periodic background sync is explicitly not designed for events that need to be triggered at a precise time, which would be needed to make an alarm clock useful. As per the original proposal:
What periodic sync is not
Periodic sync is specifically not an exact alarm API. The scheduling granularity is in milliseconds but events may be delayed from firing for several hours depending on usage frequency and device state (battery, connection, location).
The results of a sync running should be "beneficial" not "critical". If your use-case is critical, one-off syncs or the push API may serve your requirements.
There are various optimizations baked into modern mobile operating systems to minimize power usage when a device is considered idle, including running periodic tasks in staggered batches instead of given those tasks fine-grained control over when they're run.
