Most of the time, no, these elements are pretty resilient. Since these are made of an Incoloy 800 alloy, they carry a higher resistance to heat and oxidation than standard stainless elements. This means it's a lot harder to damage them than your typical heating element.
These elements WILL develop a dark gold to burgundy to black patina on them over time, and depending on how protein-rich your mash bill was or how long the dry fire lasted, this process can speed up. Below are two examples of this. These elements can usually be saved, provided that the element has not split and will still turn on.
Usually, an overnight soak in PBW or Exchilerator Brewery Wash is enough to break up any of the hardened carbon. Take some Bar Keepers Friend powder (oxalic acid) to the element outside the kettle (DO NOT TO USE ON ETCHED GALLON MARKINGS OR LOGOS.)
If that is not enough to get cleaned up, return the element back to the kettle. Heat your brewery wash solution up to about 160F for an hour or two and that will usually return these nice and shiny! If you have any questions or your element no longer heats, please feel free to reach out to Ssupport.