Of course there are mechanism to quantify the effects but you would need to ask someone from a carmaker marketing department and he would not tell you anyway.

Unfortunately you didn't get the main point which is the brand awareness. It's not that much about a particular model of the car but about a brand as a whole. Simply put in ideal situation the brand reaches a state that the first car brand which comes to your mind whenever you think about cars is the one. And that works. You never buy a thing you never heard about. So the first thing to do is to get into the memory of as many people as possible. People remember much more something what is connected with some excitement or other memorable event. And that is not an advert which just cut your favourite movie or an album on youtube.

Adverts are boring as fuck, many people outright hate them, mostly skip them, install various ad-blockers etc. But when you go to the stage you go there willingly because you want to see that. Same when you watch a video from the rally. People even buy adverts in such events (yes, the team merchandize is nothing but an advert which people pay for). So the rally itself is an advert but much better working than what people generally consider to be an advert.