Apparently Caleb upset some people with his post yesterday about a "point-shooting" video. I tend to agree with him, since I like to hit what I'm shooting at, be it a steel plate or a guy charging at me with a knife. Can you hit stuff without sights? Of course you can. A couple summers ago when I was shooting a decent amount of trap I actually used a gun with the bead removed more than a few times and would still get 20+ out of 25 clays (we found some scouts actually would worry too much about sight picture and not following the bird, so removed the bead on one of the guns and taught them to "cover the bird" with the muzzle. For some scouts it worked, and their hits went up.) However I hit closer to 25 with the bead in place, and I sure can shoot a pistol a lot better with sights than without. Those little knobbly bits are on the slide for a reason.
For me, the key is good form with a good press-out, and your muscle memory will bring the sights in-line with your intended target almost as fast as just pressing-out and hoping. Of course this means that you actually need to practice... a lot. And that doesn't sell class seats like "Learn to Shoot Fast and Accurate NOW!!" tends to.
Also, having a newer shooter taking pot shots into rock at 10 feet with no eye-pro tells me what sort of instructors they are, and that is the kind I don't want to be around.