I've had the privilege to see the expedite function does it's thing twice, and yes it overshot green dot on both occasions and without our intervention, surely it would have gone right to VLS, not pretty at high altitudes.
Speaking of which, I've seen very few captains whom I fly with use the technique of reducing the speed progressively to the best ROC or AOC speed whichever the case may be. Most just select the speed they speed they want right away, leaving the aircraft increase the rate of climb and run out of energy shortly thereafter. I have no hard figures or proof for this, but surely reducing the speed progressively is more efficient?