Daniel, shutter speed only affects ambient light, and has no bearing on the flash exposure. When dealing in 'normal' flash photography, the shutter speed has no affect at all on the final image.
If you were to shoot an indoor scene that would require a shutter speed of 1/15, but instead use a flash and set the shutter speed to let's say 1/250, all that will be captured is what's illuminated by the flash up to the distance that corresponds to your chosen aperture. You'll also get some underexposed stuff from the fall-off, but for argument's sake, it's the aperture that determine's the amount of light captured.