1. Typical springer end-to-end mechanical efficency = ME / Cocked_Spring_Energy = 1/3.
2. Fraction of springer energy derived from combustion = ~50%.
So even if you assume that debouncing would double pneumatic efficiency, losing the boost from combustion would essentially cancel out the net effiency gain and power would remain unchanged.
However, I agree you're 100% right that recoil should be dramatically milder even if the mainspring power was unchanged because a lighter piston could be used (reducing primary recoil impulse) and, without bounce, half the secondary impulse would disappear.