I don't think this works any better than the reverse (starting lighter, ending with more weight/fewer reps), or a few sets of constant weight (after warmup). It's a well known variation.
It seems feasible it could work better. If you lift an X lb weight until you cannot lift it anymore, and then drop to X/2 lbs, you can lift again, and can drive your muscles even further into exhaustion.
We used this method in high school (called it burnout then) and it never ceased to fail that a pretty girl would walk in when you got down to the bar and could barely lift it!
