The answer will not be the same for every college.
You can look at the common data set for each school (google “common data set XYZ university”) and look at section C to see if demonstrated interest is taken into account at a particular school.
Even for schools that track demonstrated interest if a person lives far away the college does not expect that everyone can fly in to visit. There are other ways to demonstrate interest such as: requesting an alumni interview, going to a local presentation, taking part in online discussions with admissions etc.
FWIW I do know a number people who got into top schools including Ivies, Wash U, Hopkins without a visit.