Yes, but if you don't have an Apple ID, the iMessage app will use SMS/MMS, not the proprietary encrypted Apple messaging protocol. This can be tested easily: send a message to another Apple user: it will arrive as a green SMS message, not a blue Apple messaging message.
Promise all you want, but in the US you can’t activate an iPhone without an Apple ID. Yes, you can set iMessage to only send/receive iMessages using your phone number. However, you cannot set it up in the first place without an Apple ID.
