http://www.factory-servicemanual.com/wp-content/uploads/2009/06/car-differential.jpg
Look at that pic and see what happens when you hold the ring gear/carrier from moving (locked by the driveshaft/transmission). Note the blue spiders still spin freely and allow the axles to move unimpeded, provided the wheels are allowed to turn in opposing directions (eg: one off the ground).
With an LSD it's different, you'd need enough force to break the clutches loose.
No.
If only one tire is off the ground, and the drive shaft is locked (e.g. in park) the tire off the ground is NOT going to spin.
You have 3 things that move in the diff, and 2 of them have to be free for any movement to happen.
Either: Pinion is locked, then the spider gears will spin and both axles will spin. (opposite directions)
Or: Pinion unlocked, (neutral) one tire off ground, other on ground, turn tire, pinion WILL move, because the spider gears will both spin AND rotate as the carrier itself moves. And the carrier can't move unless the pinion is free.
But if 2 of the 3 are locked, the other one is not going to move. So you can leave it in Park, raise one tire, and it will not move.
Edit: In summary, one rear tire off the ground, trans in Park, tire off ground will NOT turn, at all. It is locked. Unless you are macho enough to make the other tire turn with all the weight of the car on it using a lug wrench. (unlikely) But the diff will not freely spin unless 2 of the three can move.
I just went and tried it on my Jeep, which happens to have one side in the air and no drive shaft. Stuck the axle in it. Put a pry bar between two studs. Had the wife pull on the bar while I crawled under the Jeep and held the pinion.....as long as I held the pinion, the axle in the air would not move. The other side has the tire on it and is on the ground.
The differential is an ARB air locker, which is obviously not locked at the moment, so it functions as an open diff.