Of course it can make a differnce. Depends upon the school, depends upon how strong that connection is and how influential the parent/student is.
Compmom, your daughter should have checked the box, as it would likely have put her is a different admissions pool where her chances likely would be at least slightly better most of the time. If she applied, she’s likely qualified to get admitted, but most qualified candidates do not get into the highly selective schools. One point in the accept column could be what makes a difference in admissions vs wait list.