If you visit a campus with your (or as) a prospective student, be sure to take and register for the guided tour. Signals of interest like these are absolutely a factor during admission season. If you go and dont let them know, you are wasting part of the opportunity. Already taken the tour and want to go for a second or third visit then arrange to speak to a faculty member about the departments you are interested in. Your department of interest almost certainly has prospective student days. Try to time your visit with one.
Really unlikely for these kind of stats to ever be a deciding factor. Massive waste of time from an ROI factor excluding the fun in visiting. I can only see it mattering for a mid tier “safety” type school trying to boost their accept/decline rate by denying obvious safety school applicants.
Some college rankings place importance on vanity metrics like acceptance and matriculation rates. This is a reality. Top colleges are typically more sensitive to and interested in optimizing for these measures.
If you think that signaling intent as a student is not important, you are of course welcome to your opinion.
Just wanted to point out that while demonstrated interest is certainly a component in college admissions (like it or not), but varies from institution to institution on its importance.
Quick tip: if you're wondering whether a school actually considers demonstrated interest, you can Google up "[school] common data set" (without quotes). Look for Section C7, which indicates the relative weight of the various admissions factors. Just throwing it out there.