I've done something similar, drilling a pilot hole all the way through a screw, so that I could get a screw extractor in there. It worked out well, but of course I did not care at all whether the screw had any remaining structural strength, so I can't speak to that part.
What I did learn is that you want to have the screw in something that can be clamped firmly, and perfectly level in all directions. I suppose you'd want to build a jig. Also, a drill press is a much better tool for this than a freehand drill. My dad can do it with a freehand drill, but he's experienced and gifted in this area.
I'd have a spare screw or two handy, in case there's some learning curve.