2001 Dodge Neon 3-speed auto as towed

You can do exactly as you proposed. Start the engine, put it in neutral and just tow it the short distance. My friend has towed his honda crv all the way across Nebraska with the engine idling. He had stopped at a rest stop and started the engine, ran it through the gears as prescribed by Honda for towing---but forgot to turn it off. So you can easily do it on purpose for a few miles. Good travels.