Depends on what type of case we're talking about. In a civil case, the short answer is probably not. If a driver is texting and causes an accident, it's hard to imagine there would be any dispute as to liability. So, if a case like that ever went to trial, the attorney for the driver would admit that the driver was responsible, and the video would probably not come into evidence. The idea is that the video is largely irrelevant because the driver already admitted fault, and to show it would be unfairly prejudicial to the driver because the jury would likely use it against the driver in awarding damages to the injured person. As a plaintiff's attorney, I would try my best to get it into evidence, arguing that it's relevant to show the severity of the collision, injuries, etc., but it probably would not be admitted into evidence.
On the other hand, in a criminal case, it is much more likely to come into evidence.