Yes, you can travel with your hedgie however you want...
However...You also have to think about the "what ifs". If there were ever an accident, or a need to do a hard break. You have your seat belt to keep you from flying forward, and in your shock, and sudden breaking, your hedgie will end up flying out of your hands, and off to who knows where(and suffering probable life threatening injuries in the process). Also, EMS are trained to look for pet carriers, not random piles of cloth, boxes, etc etc. So if you are ever knocked unconscious and unable to tell them there's a hedgehog in the car, your hedgie will be left in the wreck.