Can sour cream be whipped

I don't think so. In the mayonnaise case, all that has happened is the fat has come out of emulsion and gathered together again, so you can re-emulsify it. In the whipped cream case, you've started to create large fat crystals (butter). I guess technically it might work to heat it up to melt the butter, re-emulsify it into cream and then beat it again, but I don't think it would be worth the effort. You could go ahead and finish churning it into butter and buttermilk if you want to avoid wasting the cream.

http://www.goodeatsfanpage.com/season1/Chocolate/ChocolateTranscript.htm

As Alton describes. As you beat the cream bubbles of air get worked into the mixture. The beating makes the bubbles smaller and smaller until the fat globules touch and the mixture becomes stable.

As you mentioned- if you whip it a little more then the fat will coalesce and squeeze out all the water and air and you have butter.

Time is a factor in this process (when done mechanically) in that it is required for homogeneously sized and distributed bubbles. The fats have to stay plastic.

The fact that it can be done very quickly is easily seen with whipped cream chargers. The gas is pressurized into the cream- upon release expands into the tiny bubbles we need.
How does a whipped cream charger work?