In deed, each Rig is loaded with its Base Sound regardless of the current position of the Morphing controller and regardless if the module is locked or not.. However the Base Sound doesn't have to be "0" as @paults indicated.
If you would send MIDI control changes, another Rig would also be loaded as stored, except if the module is locked OR you have a MIDI foot controller, which automatically resends control changes with their latest values after each program change.
Perhaps we should change perspective. If you are sitting in your studio.and want to maintain all effects and their current state while just browsing amps or cabinets or stacks, selective browse would be the way to go. Bring the stack into focus, turnt he BROWSE knob and select "From Rigs".