"What will happen?"
Some places will turn them down; some places will be fine with them staying at their place. Most don't/won't care. And who really cares? I did this when I was younger and I stayed in parks and on the side of the road or anywhere I could. I even broke down a few times. I didn't care; I was young and having fun!
They will have a great time and make many memories. They might break down 2 miles down the road; they might go the distance with no mechanical problems at all.
There is a big lesson in this small film clip."Oh what I would give to be young again and do something like this"; T&P. Get to livin or get to dying, your choice. :)