I can't speak for New Orleans, but yes, you can get off at DC to watch the engine change. However, head the warnings. They have been known to leave without passengers. Since WAS and points north are "discharge only" it can leave without much warning.
Have you ever been left? My experience in a bunch or engine changes on the Crescent has been that the engine change is so obvious when it is complete that you can't miss it if you are on the platform. Also, the car attendants will remind you to get back on the train. The only chance of missing the train is when you leave the platform.
Thanks so much for the info I got a room at the Holiday Inn down the street just in case.
We usually stay overnight at the Quality Inn which is highly rated in Tripadvisor and closer to the French Quarter. Remember, there is a trolley that runs from the station. It's like $0.70 for seniors if you qualify. It runs within 2 blocks of the Quality Inn but if you miss it, the walk is not bad (2 overweight seniors did it a few times). We never felt unsafe. Last trip was in 2014 - Crescent from Atlanta to El Paso on SL and return.
There are also plenty of taxis.