A leaf shutter has sync on all speeds. A focal plane shutter on the other hand, usually has a max. sync speed that is much slower than its fastest speed. Both, your leaf shutter and your flash are not “digital” in their operation. Light intensity increases as the leaf shutter opens and decreases as it closes. When the flash is triggered, it rapidly reaches its peak light volume and then “burns out”. Both processes take place within fractions of a second and usually cannot be observed with the naked eyes. While the focal plane shutter has a very small time-window when both curtains are open, the flash light might not have finished when the second curtain start to close. This is not the case with a leaf shutter. Although a leaf shutter may cut the flash, too, the effect will be an underexposure but not a partial exposure as it would happen in case of the focal plane shutter.
The specs of a studio flash usually contain one or two of the figures “t 0.1” and “t 0.5” (usually for max. load). These figures specify the amount of time the flash needs to reach 1/10th (or 1/2 respectively) of its maximum intensity after being fired. The values for t0.1 can be as long as 1/60s for very powerful flashes and is usually shorter than 1/500s for lower energy or compact (battery) flash lights.
The shutter speed is usually determined by the desired amount of ambient light in the scene. The longer the shutter speed the more weight is on ambient light, as long as the flash energy stays the same.