No! According to the Department of Transportation, responsible for overseeing and regulating the auto transport industry, it is forbidden to ship a car with personal items. Federal laws also support this rule.
Violation can attract a fine of up to $10,000 for the auto transporter. To avoid such fine, auto transport companies have the "No Packing Policy" as part of their protection. Also, the amount you will pay for auto transport depends on the overall weight of your car and having additional items in will not only increase the weight but also tip off the auto transporter.