The problem may be everyone's definition of mountain biking is a little different. I've done some races where drop bars would have maybe made me faster.. but then I would suggest that I was just using a mountain bike in a cycle-cross race. There is nothing wrong with that really, but mountain bikes were designed with more difficult terrain in mind.

Bike handling has less to do with the shape of the handlebars and a lot to do with the position of the rider. On technical trails, there is no question that having your weight further forward and you hands lower (which I think is the point of a drop bar) makes the bike more difficult for me to handle. I've never actually put drop bars on a mountain bike, but I have ridden cross and road bikes on dirt, and I just can't ride over roots and drops with my weight that far forward. On smoother trails and wide-open roads, I'd say the drop-bar position is faster ... although a flat bar on a negative-rise stem is almost as good, albeit with less hand position options.

But to answer the original question, if you are seriously thinking about putting drop bars on a mountain bike, you are probably not using it on trails where you are at risk of pitching over forward. Go for it.