Yes, for most sports a recruiting video is crucial for a college coach to evaluate you as an athlete. For many coaches, this is a required aspect of any recruiting resume, if they are going to take any interest in you. Some sports, like swimming, track, and rowing, rely more on event times and meeting results, rather than video. But it is always highly recommended to have some sort of video footage, in case a coach wants to see it.
Having a highlight video or game footage is very important to college coaches, and unless you make it very easy for them to view, you are not going to have a successful recruiting effort. Having video ready allows coaches to be able to watch you play without having to spend money on travel. What they see in your video will help them determine whether or not they want to come and evaluate you in person.
It’s not enough to send a coach a sheet of your statistics from your season, they need to be able to see your technique, physicality, and skills and the only way to do that is with video.
A coach isn’t going to recruit an athlete that they haven’t been able to see play.