What time stamp will show when an iMessage is received while phone has a dead batter / is turned off? 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?
I'll will show as sent at 3:45. 

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