Yes they do, a lot of police departments have software that can enhance video, like the software below:
Video Enhancement Examples | Amped FIVE
However, they might not use it for property damage cases. I don't know what extent they can search DMV records, but with the vehicle model (Obviously a Honda Odyssey) and a partial plate number, they may be able to narrow down results by a lot.
In my search, I found a video tool that claims to be free:
VideoCleaner FREE forensic video enhancement software - Finalizing