Yes, they can charge you. The only time that your rights need to be read to you is when you are in custody, and the cops want to talk to you. If you are not in custody, or the cops do not want to question you or do not care what you have to say, then they do not have to read you your rights. The Miranda warnings are only to insure that statements you make in response to police questioning while in custody are admissible in court.
