At every program I’ve worked we’ve gotten daily calls, letters and emails requesting a questionnaire. This isn’t usually a helpful or efficient way to get on a coach’s radar, particularly at many Division I schools. Again, the only true way to get the school to recruit you is if they see you play in person or on video.
The exception is if a school SENDS you a questionnaire, a questionnaire that you didn’t call and request yourself. You should definitely fill it out and return it, it means they have gotten your name from a trusted source and want to do some more research on you and may contact you at some point.
On the flip side, when you call and request a questionnaire, it may not get looked at or added to the database when you return it. When people request questionnaires they are often coded before they go out and are not always evaluated when they are returned, particularly at more competitive schools.
Cut to the chase and send your film!