Ah never thought of that.
It didn't when I tried it ages back with a Nikon - there was a drop off as shutter speed increased. I suspect it gets hit by the first or last pulse from the gun and the power of this decreases as the gun has to make more flashes to cover a shorter duration. But then each bit of the sensor only gets hit by one pulse so my guess is that it would average out.
It's complicated, and it varies! But either way, the loss of effective exposure is very substantial with high speed/FP sync. Here is the maths
This is how normal flash sync works with a typical focal plane shutter - and these numbers won't be far out for any camera with an x-sync around 1/200 - 1/250sec. First curtain starts, and take about 3ms to get to the bottom of the frame. The whole sensor is now uncovered and it then waits for 1 or 2ms, during which time the flash has enough time to put out its full power pulse - 1/830th of a second in trhe case of a Canon 580EX. Now the whole of the sensor has been exposed by flash and the second curtain can close, taking another 3ms to cover the whole sensor again. Total shutter cycle time about 8ms.
The difference with high speed/FP sync, is that the flash must put out light continuously for 8ms - about 8x longer - because some part or other of the sensor must be exposed to light for the whole of that time. The flash duration has to be increased by about eight times. In practise, the high speed sync pulse starts fractionally before the shutter even starts to move, and stays on a bit longer, just to be sure. It is actually continuous light, for that brief period of time.
That's how is works in principle but there is obviously room to improve on that. A camera with a faster x-sync speed takes less than 3ms to travel from top to bottom, so the flash doesn't have to burn for so long. And at faster shutter speeds it obviously doesn't hang about fully open at all, and the time between the first and second curtains travelling gets very much smaller (that time is your actual shutter speed and effective exposure time).
So if you had a very fast shutter (eg Canon 1D4 with x-sync at 1/300sec) the travel time for the curtains might be cut from 3ms to 2.5ms, and at say 1/1000sec (1ms) that would give a total shutter cycle time reduced to 6ms.
While that might not seem much different to 8ms, a saving of 2ms actually makes a big difference to the exposure. Therefore if the flash can be configured to burn for less time, and the energy concentrated into that shorter burn time, then you'll get more light. And as shutter speeds get higher, the (very fractional) benefit increases.
That how PW's optimised high speed sync works, with the HSS burn time customised both to individual cameras and also to different shutter speeds. With a 1D4 at certain speeds, they can save a stop over the regular Canon system. I don't know how Nikon does it.
As an aside, here's an interesting slow-mo video on a Nikon D3's shutter at work, with timings. Pretty amazing!
http://regex.info/blog/2008-09-04/925
£££
There's an overlap with HSS and you can shoot with either at 1/200sec, and that's what it is - with that camera, and that flash, at that speed.
