I noticed a similar issue recently when I turned wifi and mobile data off.
I was troubleshooting a problem where Google Messaging had a running service "Messaging Transaction Service" that was holding a wakelock for hours causing increased idle battery drain. Using WLD I saw the wakelock was related to MMS, so I turned on my mobile data. This didn't immediately help, so I forced close the Messaging service, and I then immediately received the MMS. Up until that point, I had no notification that a MMS was pending.