Yes, I would help an injured stranger and in fact have done so on a couple of occasions. Whether or not I know a person does not determine whether or not I can and will help them. The world is a much better place when we all decide to help those in need.
Many injuries are severely worsened by mentally being alone... Therefore, whether the injury is big or small, life threatening or not, self inflicted or not. Many will survive or get the necessary care simply by having someone there. Also being nationally certified to perform first aid, my personal integrity would not allow me to pass up the opportunity to save a life.