Rumor has it that they are going to do bike checks on the course. So fitting in would be important. Not having a number plate might get you unwanted attention. Like you say, the roads are open, but that might not stop a course marshal on a motorcycle from power-tripping for more time than you want to spend arguing in French. I would be curious if you have to explain yourself for the aerobars. They are legal for official riders as long as they don't extend past your brake levers. You have to have reflective gear. They started including their reflective gear in the entry, so everyone has the same reflective vest. If your lights aren't up to their standards they may harass you for that. Food might be an issue.
There are actually companies that have group rides on the course. So you wouldn't be alone. But from what I've seen, they ride in groups.