I think for iMessage, the actual messages are sent using APNS, so the message is in the push notification itself. Thus while you can see the message itself without unlocking, any older messages that are behind the Secure Enclave are inaccessible without keys.

This is correct. For example, when I connect my iPhone to my provided work wi-fi, and I get a Tinder notification. I can partially see the message on the lock screen (once Face ID authenticates), but as Tinder is blocked on the wi-fi if I want to read and respond in the app I have to pop to cellular.