And the next question is, is the result any different than if you were to just hook it up and carbonate it? The only thing I can think of is that some of the yeast in suspension would drop out and the beer would be (a little) clearer?
That does happen, but it is affected by a variety of factors, such as type of yeast used. And it's a tiny amount. My experience is that primarily it doesn't affect clarity in my brewery. If a brewer is brewing lagers, filtering, fining or clearing their ales intentionally before
carbonation this technique wouldn't make sense. It's not appropriate for everyone, but a tool to be used.
Tell me though, are you seeing any sludge in the bottom of your kegs when you open them after the last beer?