I do it all the time. Especially the white crayon on dark fabric, but I've worked with all of them. They come out no problem every time. The only "downside" is that the line is thicker than with the markers. I definitely haven't ever touched it with an iron (though I have done that trick with candle wax). I don't know the science behind it, but having worked as a 1st grade teacher & a nanny to 2 preschool children for a number of years, I can say with 100% certainty that I've removed the Crayola Ultra Clean crayons from clothing & cloth furnishings more often than I care to admit. I stock up on boxes by the dozens when they go on clearance because inevitably the crayon doesn't just end up on the children's clothing, but on mine as well and I want to be sure to be able to get it out.
And actually, most of the tailor's chalks are made with wax & those certainly come out without ironing.