What time stamp will show when an iMessage is received while phone has a dead batter / is turned off?

Question

An iPhone has a dead battery. While off, an iMessage was sent at 3:45pm. The phone was recharged and turned back on at 5:00pm.

Will the iMessage come through as being sent at 3:45pm or 5:00pm?

Answer 1

I'll will show as sent at 3:45.

Your phone only matters in terms of the message being delivered/read.

Answer 2

The message will be marked sent at 3:45, but not Delivered... unless:

If you have

1. Messages running on your computer, or
2. your same iCloud account as an active profile on a computer,

then the message sent at 3:45 will be delivered to that device.

iMessages are not restricted to iPhones.