You're talking about shutting down Washington DC. What do you honestly think is going to happen? Tickets? Horse****. There's not a chance in hell the Federal Government would let that stand, nor any of the local (or state) jurisdictions that are covered. It would invite more of the same. If those guys do park their trucks in the road to completely stop the Beltway, they'll be made an example of using whatever rationalization the various police agencies in the area can make up. Fairfax County cops don't care what the law is on the average day, and if these guys try to screw up Fairfax County, the cops will care even less what the law is on that particular day. DC cops, and the various city police forces, plus Maryland and most likely Federal police agencies will all be getting their slice of the pie. You can't just close Washington DC and not expect every police authority within the Beltway to respond. That's just plain naivety. That's not the way these assholes do business. Especially not in the specific areas that would be affected. They can try to argue the letter of the law all day, but they'll be ignored and tossed in jail. If you doubt that, then you obviously don't understand reality.
Also, these would almost certainly be empty trucks. If they have freight to deliver, they're not going to spend an extra 3 days circling DC, and they certainly aren't going to park to stop traffic.