Which macOS processes handle iMessage network communications?
iMessage message delivery is not as such handled seperately in a specific process for that single purpose.

Instead the generic apsd (Apple Push Notification Service Daemon) process handles the network communication. apsd handles Apple's push notification service in general.

The imagent process that you have already identified is indeed involved in iMessage, and not only Facetime. It is there to receive the notifications forwarded by the apsd process.

In addition there's a special case for iMessage attachments (i.e. very large iMessage messages in general). Their content is not transferred using push notificcations via apsd, but are rather downloaded from iCloud. That process is initiated via a notification from apsd however.

All in all this means that you can kill the apsd process, and keep it from restarting, and thereby stop iMessage messages from coming in (without "deactivating"). However it would also stop any other push notification from arriving at your computer.