Unlikely a dash cam would have such a wide field of vision. Given most are mounted on the inside of the windscreen, it would require more than 180 degrees to "see" the door. But, most dash cam have a sensor to start recording if the car is hit. Assuming the car which hit you was passing from the rear to the front, you should be able to get the reg of the likely culprit. If the car was passing from front to rear?, maybe, I think some will start the recording from 10 or maybe 20 seconds before the impact.