Clogging up heating surfaces is sort of like having all the traffic lights in your town turn red at the same time, and then stay red. Most movement just stops. In the case of boiler sludge and scale, that movement is heat. It's trying to get from the fire, through the metal, and then onto the conveyor belt of flowing water but sludge and scale can block the way. So the boiler just keeps getting hotter as the building gets colder, and that's not good for either one.
Simply put, pipe sludge is nothing more than rust that flakes off the inside of the pipes. It will just go with the flow into the places that will cause you the most grief. Get enough of that sloppy stuff flowing around and it will gum up the whole works.