I am a college tennis coach at Drew University in Madison, NJ. Although we love to see kids who play tournaments since it gives them good competition and practice dealing with adversities on the court, schools that are not giving out scholarships, such as D3 or many other schools at other levels that don't have them, the tournaments aren't as important. Unless you talking about an elite program, there will be open tryouts that will allow you to show what you got against the current roster and other freshmen. Tournaments and rankings may put you on a coach's radar, but unless you are in search of an athletic scholarship, it isn't really necessary.
Ex-Coach: U of Delaware & Drew U. Pro Kennex Ki-5(R) & Gamma RZR 98 (L)
Dunlop Black Widow 17 (63lb) Babolat N.Vy 16 (64lb) USTA 4.5.