I might be wrong but, i think...
When the screen is unlocked, 3g is enabled, send your message, JD will detect the traffic, if you lock the screen during that time after sending it, the badge in the notification bar will show an orange dot and have MMS underneath, if you are using the widget, it will detect the traffic and let the massage finish sending before disabling the connection, you might have to play with the data traffic thresholds, or at least this is my experience with it.
If some sends you a MMS while the screen is locked and 3g is disabled, you will get it the next time you unlock the screen and 3g is enabled, our when your scheduled event occurs, whichever happens first, might have to play with MMS connection settings, and/or the auto download settings, you might have to set it as making you a ask to retrieve (download) the message, or at least this is my understanding off how all this works, if MMS is 3g controlled and not network dependent.
Too bad i have a grandfathered in 20$ unlimited data plan left over from now totally absorbed Centennial wireless, i still use JD for battery saving power, with very light use last weekend, i got 2 days and 12 hours before getting to 15%. To me that's unbelievable for a Android smartphone