I understand the thought behind the pull-ups but in my experience it prolongs the whole process. In the last 10 years, I've toilet trained close to 30 children without them. By day three, it's incredibly rare to have a mess. I can't imagine a whole month of the process.
Different folks, different strokes.
That is pretty much my experience too. If they are old enough to potty train, then they understand quite clearly that a pull up is a diaper. Also, if in big kid underwear and pooping and peeing all over the show, the chances are, toilet training was started to early.