Technically, it should work... but keep in mind that the balance on the elevator will change with a dynamic CG configuration (think of pitch changes on a hang glider to visualize this).

The ideal situation will be when the CG moves from a slighly downward force on the tail to a slightly upward force when the CG is moved backward (this should keep drag to a minimum). An all-moving horizontal stab would be best.

You could do this in a glow/gas powered craft by locating the gas tank far forward and carefully balancing it so that when the gas tank is empty, the CG moves back no farther than the rear CG limit. In this configuration you would need no servo control, just careful planning! The bad part of this is that your CG is constantly changing.... so the aircraft dynamics are constantly changing as well. This type of setup would also require that the fuel be a significant percentage of the aircraft weight so that this "slide" in the CG is significant (this may be very difficult to figure out).

So, doing this with an electric craft would be much much simpler!

There are a few full size craft that needed a great deal of pilot input during flight to balance out the aircraft. The reason for this was because the fuel tank could not be located near the CG due to structural limitations, etc. And no, I can't think of which aircraft had this problem/feature off the top of my head.

Good luck!