My Pentax 645NII has been mountain biking, hiking, rafting, xc-skiing and snowshoeing. I've shot in all conditions from rain to dust to being as cold as -40. I take no special precautions other than a padded case or a drybag. So on the whole I would say it is a pretty skookum rig.
But not sure about the extreme dust and other aspects of Burning Man. That sounds like camera death to me. I'd probably hit the thrift store for a bag of cheap film cameras and just have fun with 'em. Either that or buy a couple of old land cameras and bring a tote full of Fuji instant peel-apart film.