I've not greased the groove with 10-20 swings, but I'm giving it a try, along with easy sets of 3 dips.
Pavel did not elaborate on what body comp and conditioning benefits might accrue, but I remembered as I read this that in Tim Ferriss' 4 Hour Body book, it seems that I read that as little as 30 seconds of intense activity can release hormones, including testosterone and HGH, along with something else (GLUT something?). He recommended pushups before eating to release some hormone that burns fat. I don't have the book in front of me- perhaps someone else can elaborate.
Perhaps the benefit of GTG swings come from frequent bursts of hormonal stimulation, which keep overall levels of muscle-building, fat burning, appetite suppressing hormones elevated above what they would normally be? Can someone with more expertise in this area fill in some details?