Technically yes you can make a reflector without height, called a flat mirror, however the focal point would be at infinity so your LED would have to be inifitely far away.
You can make a shallow recoil reflector, with very little depth, and as long as the LED is at the focal point yes it would throw the same distance as a deep reflector with the saame front area.
Play around with the Reflectors #1 and #2 changing their diameter and focal distance, you will see how the parabola changes shape.
While the depth of the reflector changes how many lumens are collected, the frontal area is what determines throw.