This idea occurred to me several months ago too. So I brought home my near-the-end-of-it's-life-cycle-unibit and fired up the old dremel. I did the best I could to keep the edges straight, but without some sort of a guide it's quite hard to do. Also where the bit steps to a larger diameter it's difficult to sharpen the edges while maintaining the proper angle of the step...difficult to describe...difficulter to do. All in all it was not an easy task. The results speak for themselves: The bit now works fantastically well! (for making holes in drywall.) And it was nice to finally use a sharp unibit...when I picked up a replacement.
I was doing some work in a machine shop so I asked if they would be able to sharpen a unibit for me. Apparently it would take about 2 hours to do and it would cost more than a new bit.
I agree with Gibbons and make a pilot hole first and then switch to the unibit. It prolongs the life of the tip at least.
I also have a plastic case from a short auger bit, about 3" or 4" long that I store my unibit inside. Then the bit's cutting edges aren't bouncing around hitting stuff and being dulled in my tool box.

Shawn.