This would be a bad idea, tacically and economically. In a protest, at least in the U.S., you can take measures to protect your identity and not carry any documentation, along with the ability to flee on foot in any direction. You also have no tangible assets on you that the government can seize.

In a vehicle protest you forfeit anonymity (lincense plates), ability to split since road-blocks can easily stop you, and most importantly your vehicle might be impounded.

OH it would work. And it's nearly impossible for you to get into trouble. If all the protesters just drove in a circle such as getting on the highway at a specific ramp and getting off at a specific ramp just to get back on. They would create a massive bottle neck not only for those 2 ramps but for the roads that connect to them. There's no law that says you can't joy ride or that you must avoid congested traffic. A group of only 100 people could very easily find a bottle neck on their local highway and exploit it.

In some places, "Disrupting the flow of traffic" is illegal. For example, driving at 55 mph on the highway is legal. However, driving next to someone, both going 55 mpg, would be illegal, as it disrupts the flow of traffic.