Can only answer on the 930
If it was last playing an mp3 on the sd card, I can hear where it left off while in the splash screen process(about 10-15seconds), after that you'll have the capability to change from the menu IF it wasn't on the GPS function, then you'll need to wait for the 'warning' to get past that then the main menu. I try to remember not to leave it on the GPS before turning the vehicle off. Steering wheel controls work to change to next, begining or previous track, depending how many time it's pressed. Same for am/fm.
Not the most user friendly HU in my opinion.
hope