Can car accident straighten your cervical spine?

Yes. It's called cervical strain and due to muscular tension. It can be alleviated with formal physical therapy.
Yes. The crevice spine straightens when the muscles along side the spine are more active. This happens when a "whiplash" type injury occurs and the muscles and supporting structures of the neck have been injured. Straightening of the cervical spine is not dangerous, just an indication that there has been an injury.