If I bend my torso toward the top bar, lowering my center of gravity, will that alone help my bike go faster?
Speed depends on your power output and your drag (see How can one estimate drag for a bicycle? for a full explanation). If we are considering a constant effort without wind, your flat land speed is determined by your power and your drag, which in this case will be made up made up of aerodynamic drag (i.e., frontal area) and your mechanical drag (i.e., rolling resistance).
Lowering your body will affect your aerodynamic drag. If you keep your elbows tucked in (or arms forward and elbows tucked in), your frontal area should decline, which could mean a faster speeds if you can maintain the same power output. However, depending on how low you go, your flexibility, and your experience with trying to do work in this new body position, your power output could be affected which could undo your aerodynamic gains.
If you follow through How can one estimate drag for a bicycle? we can see that in this case the power required to overcome the aerodynamic drag is directly proportional to frontal area (CdA) for a given velocity.
watts(aero) = 0.5 * rho * CdA * (speed in m/s)^3
Because power output can be affected by body position, the question then becomes does is the percent change in frontal area (CdA) from lowering your body smaller or larger than the percent change in power that results from the position change.
This question isn't cannot be generally answered as we don't know the positions your are considering (other than it is "lower") and we don't know how your power changes with your body position.
The best thing will be for you to directly answer your own question by setting up a small field test, where you time yourself along a stretch of flat road (ideally without wind) in the different positions. I would personally want to replicate each run a minimum of 3 times and take the average then compare. In a similar context you could also set it up as a paired design, where you test each position in pairs, but randomize which position is used in a given pair. The pairing allows you to include some control for changes in environmental conditions over time. What ever you do don't run all your replicates in one position, then the other as you will have confounded your treatment effect with time (i.e., where any changes due to changes in environmental condition or your setup?). Randomizing the starting position allows you to control for confounding variables such as weather.
You then take the time difference and test against a null hypothesis of zero using a paired t-test. This will let you know whether or not any difference you observed is different from random chance. I would default to a "two-sided" alternative, which means we are potentially interested in speed differences in either direction (i.e., lower or higher body position is 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.
Not like I see it. I remember reading on wind tunnel results in the 90's that concluded being narrow is more important than being low.
COG doesn't have an effect on speed as the real problem is wind resistance.
Here's an interesting review. Section 4.1 delves into body position. I'm not shocked by the idea, but surprised to see by how much drag can vary between riders. That paper describes a difference of 30% on two test subjects.
It also shows that for a particular rider, the drag was at its lowest while he rode in the brake horns. Frontal area was seemingly not the determining factor in his case, probably due to the rider's morphology.
There are three things to consider:
Position of Center of Mass.
Irrelevant in a direct sense. However, the posture change that is connected to this is relevant.
Very relevant. When you lower your body, you decrease the area of attack, and thus reduce the largest component of drag at relevant speeds.
However, the amount of this effect depends on the speed. The faster you go, the more important this becomes.
Posture induced discomfort.
Quite relevant. Have you ever tried to remain in a low bent position for any length of time? The lower you go, the more uncomfortable your position becomes, until it's literally more pain than its worth.
The combination of 2. and 3. means, that a low-bent position is a must if you want to set speed records, especially downhill, yet it's better to use a more upright, comfortable position when going uphill. Personally, I never bother going low unless I'm well beyond 30km/h. But above 40km/h you only see me sitting up when I want to air-break...