[shu]

It may well be that maximum efficiency is achieved if pressure peaks and combustion is completed just as the projectile exits the barrel. What is asked for here however is not maximum efficiency but minimum noise.

Clearly the projectile can accelerate evan as pressure behind it decreases. This happens every time an air gun is fired.

My grasp of thermodynamics, scarcely adequate at its best to model evan the simple firing of an airgun, has long lain dormant. However..

..if pressure behind projectile is above atmospheric, there is a force behind the projectile equal to the pressure difference times cross sectional area;

..if this force is less than friction between projectile and barrel, the projectile will accelerate.

Under the right conditions I think the velocity of the projectile could continue to increase right up to the moment of exit from the barrel, but driving pressure decrease at that point to just above atmospheric. No expanding gas behind the bullet; no noise of expanding gas.

Practically however a handgun barrel just is not long enough to achieve a useful velocity.