will imessage say delivered if other person has no service

The message will not be delivered if there is no cellular connection and no Wi-Fi connection and will not say delivered.

Depends on what you mean by no service. It will be delivered and say so if they have a Wi-Fi connection, whether or not they have cellular service. If the have no Internet connection at all it will be held for a while, and will not say delivered. If it fails to be delivered after some hours (I don’t know the actual number) it will discarded.