It is quite normal for a leaf shutter to support a faster shutter speed when the lens aperture is physically smaller, i.e. at f/8 instead of f/2.8. So the question becomes 'does the Canon G7 have a leaf shutter?'
There's a simple test for that.
Set the camera's shutter speed to 1/60s and aim it at a blank wall. Force the flash to fire and take a photo. The result should be evenly illuminated, more or less. Now set the shutter speed to 1/1000 or so, and take another flash photo. If the result is still evenly illuminated, more or less, then it's a leaf shutter. If part of the photo is black, especially if it's only one side, top, or bottom, then it's a focal plane shutter.
(There is one other option – a shutter that's partially or entirely electronic. But as the camera does have a mechanical sound when firing this is unlikely, and electronic implimentations are less far less common than mechanical shutters.)