Does the Bindon Aiming Concept (BAC) really work?
It does work; but it works better for some shooters than others. First, because the distance between your eyes is different and the tilt of your head are unique for each person, so is the shift from the unmagnified to the magnified view. In addition, if you have any form of phoria (which is common in older shooter), the shift is greater since your eyes don't track perfectly in alignment.
One thing that the Trijicon online demonstration doesn't show is that the point of aim changes slightly from weak (unmagnified) view to strong (magnified) view. This is because your brain is switching views from two entirely different angles; but using the reticle view superimposed by the dominant eye. The result is that a reticle that appears to be dead on target in the weak view suddenly jumps over a bit when you switch to the strong view (the strong view is the real point of impact if the scope is properly zeroed). This jump is determined by the factors I mentioned above.
Is it as fast at close range (i.e., under 25 yards) as a good dot sight?
No. A good dot sight is almost always faster, though with training and BAC you can minimize the difference. Check out the Reading Library thread tacked at the top of the Rifle forum for a comparison of times using irons, a dot sight, ACOG, and a low-powered variable scope by two trained shooters. The ACOG is a little slow in that one because the shots were taken exclusively with the magnified view. If we had shot with the weak eye (unmagnified view), it would have been a hair faster; but a little more uncertain where the hits would land. Since we were combining movement with shooting, it is real easy to throw them outside the desired target area using just the weak eye view.
Is the BAC a natural ability within the human optic system, or are the ACOG sights designed especially to work with the concept?
BAC is a natural human ability for anyone with good binocular vision and minimal phoria (Differences in alignment between two eyes are minimal). You do not need an ACOG to make it work. All your brain is doing is superimposing the reticle from the strong eye view over the target view from the weak eye. One thing you do need to make it work though, is good contrast between the reticle and the target. This can mean anything from an illuminated reticle to a thick post reticle or a circle/dot reticle to make the reticle easier to pick up.
If a design of the sight itself, which of Trijicon's optics offer the capability?
Any of the sights can be used that way; but the sights with "BAC" have a combination of tritium and fiber optic tube that illuminates the reticle at all times. This means that the contrast is very good and very easy to use. I imagine there are also a few trade secrets in the design that make it easy to use as the Trijicon scopes seem to be easier for me than any other optic. In most of the BAC scopes, Trijicon makes it even easier by using fairly thick, bold reticles that offer good contrast even when unilluminated.
One downside to illumination though is that if you get partial illumination and a background that is lit the same way (say a fine amber reticle at dusk, or a red t-shirt with a dimly lit red reticle), the reticle can seem to "disappear" briefly. I've never seen it in actual use; but I have been able to use an adjustable lighting system to tune the light and background just right.