Typically insurance follows a vehicle first and driver second. You will need to contact your insurance company to make sure there are not any exceptions that will keep your van from being covered under your collision portion of your full coverage policy. If there are not than you should be able to make a claim but will have to pay your deductible amount.
There is the possibility that your insurance rates could go up after making a claim. That differs depending on how your specific insurance company determines their rating guidelines. Your state's insurance regulatory body could tell you more since insurance companies must file their rates with them.