Most of the advantage is aerodynamic. If one moves from riding on the bar tops to the drops on a road bike, one immediately sees an increase in cadence, and speed, at constant effort - and this is all abput wind resistance.
However, being rotated more forward also offers some advantage in recruiting different muscle groups. Time triallists will tend to be low, and forward, so that their centre of gravity is almost ahead of the cranks.
As for the saddle, it all depends on how low you go and how you are set up at the moment. If I were you I'd proceed in small incremental adjustments and, at each stage, review whether you're still sitting comfortably. You certainly don't want to shift your weight from your sitbones to your perineum.