A new car dealership isn't going to jeopardize their vehicle sales license for some dirt deal with an undocumented crazy person. Maybe if you had some muscle, and you kicked them down an extra $15,000-$20,000, then they might try to find a workaround, but not for some $2000 profit deal. A single deal is nothing to a new car dealership, they're swimming in money.

Edit: they don't want you to pay cash anyways. They make as much or more money on the financing as they do on the car.