Ridding cooked food of burnt particles

I would think that would be fine, but keep in mind that rinsing is going to remove some of the flavor that you've cooked on to them. It is certainly safe, so long as the water is potable. I would even venture to say there's no reason specifically to use salt water. Looking at the recipe, it seems you're going to add more seasoning(and salt) after this step anyway. In addition to that, I always tend to cook with slightly less salt than a recipe calls for, so I can allow my guests to add salt as desired at the table. Always remember that you cannot remove salt from the food, and shrimp is no exception. That said, rinsing shrimp in cool/cold salt water is not likely to add a significant amount of salt to the end product, assuming you drain and/or dry them afterward.

*This is a segway to my answer, but it seems to me that the recipe is a bit misleading by telling you to boil them until "most of the gravy dries up". I would say you want to cook them until you have only a very thin layer of simmering gravy left in the pan. Continuing to cook until the gravy begins to dry up is what will result in greatly increased temperatures(hot spots) and charred particles. As long as you have water lining the bottom of the pan, the gravy should not exceed 212 degrees F(100 degrees C), and you should have a minimum of anything becoming charred. The shrimp itself would be likely to still undergo mild maillard reactions on the surfaces directly contacting the pan(which is a controlled precursor to charring).*