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.
The message will be marked sent at 3:45, but not Delivered... unless:
If you have
then the message sent at 3:45 will be delivered to that device.
iMessages are not restricted to iPhones.