Faster with lower center of gravity? If I bend my torso toward the top bar, lowering my center of gravity, will that alone help my bike go faster?
Leaning forward will help you go a bit faster, but not not because of lowering your center of gravity (more properly center of mass).

Leaning forward reduces your frontal area, which reduces air resistance which potentially enables you to go faster. However, there are many different factors that come into play that effect air resistance - style of bicycle and handlebars; hand, arm and head position etc.

Personally, I find that leaning forward reduces the power output I can produce, so adopting an aerodynmic position only makes sense on fast downhills where the aerodynamic benefits exceed the loss of pedaling power.