The guru's at Titleist can tell us exactly however It is my speculation that you do not have to have the rear weight however it does add to the swingweight, thus without it your swingweight would be very light, plus the vibration (assuming any) might be not muted with no weight on the sole.  However, like anything in golf...if it works and you like it go with it!

Good Luck

Can a guru at Titleist tell us exactly if the Rear Weight does affect our driving distance or not? Also, what is the effect relative to distance if the rear weight is completely removed? I'm already aware that it does affect the swingweight. But I would like to know if it does affect our driving distance or not? So far, I'm not able to find any answer to my question anywhere. Thanks!

The rear weighting helps mishits and alters the "gearing effect" of the face.

Now consider the pros and cons, less weight means you might be able to swing faster for more distance, but a mishit will make you lose distance. So there might not be any net gains.