quick answer: if you take a photo without the flashes firing (but all other settings the same), and the image is complely black, then a faster shutter speed will not be helpful.
Long answer: First, let's remove the all syncing limitations, and pretend a camera can sync at any shutter speed and get the full amount of flash in doing so (this statement would be impossible, but that is another discussion all together). In a completely black room (no lights at all, except for the actual burst of light from the flash), if you maintain the same ISO, aperture, and flash output, you can take a portrait of 10 minutes, 1 minute, 1 second, 1/100, & 1/1000 of a second, and get exactly the same exposure, with no motion blur. This is because the shutter speed only cuts the amount of ambient light (zero divided by zero is still zero). We don't live in such a vacuum, and ambient light will exist. Usually this is in the form of interior incadescent or flourescent lighting, which is still usually very low. Typically 1/125 of a second is enough cut the ambient light to nothing. If you wish to include some of the environmental lighting, you can lower the shutter speed to let it soak in. Outdoors, the more you raise the shutter speed, the darker you can make a sunny day, letting the flash expose the subject properly, adding contrast and drama.
Adding our limitations back in, you cannot go over 1/200 outside, so you need to reduce your aperture to cut the sun, necessitating more flash power (or more efficient flash power). This is about the only time a faster sync speed is useful.
Flash durations will vary from model to model, but the flash duration (t.1, the action stopping ability measurement) on an AB800 is 1/1100 of a second (at full power). This means if the flash is the sole (or overwhelmingly dominant) source of light, you will freeze action the same as you would if your camera was set to 1/1000 shutterspeed, thus negating the need for an actual higher setting on your shutter speeed. If ambient light is fairly high versus flash power, some blurring can occur, so be careful lighting basketball games, for example.
a few things to remember: shutter speed only affects ambient exposure flash output settings only affects flash exposure ISO will equally effect ambient and flash exposure Aperture will equally effect ambient and flash exposure
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