A picture taken
at 1/500 & f/4
or 1/250 & f/5.6
or 1/125 & f/8
with ISO remaining the same
will give you the same result (quality, color, etc.)

However higher shutter speeds can help reduce blurring caused by subject motion.

Higher shutter speeds will also reduce the DOF (Depth of Field), because higher shutter speeds will affect the aperture setting.

Let us know how your experiment works out.