Coaches in lots of sports definitely attend games and showcases to recruit. Mine were contacted from coaches of additional sports they’d played outside of their primary sport they were being recruited for, but only at schools they had at least filled out a questionnaire. If they are potential varsity level in those additional sports, the coaches may ask for film, stats, coach contacts, etc. for the additional sports if available. It definitely makes it easier for a coach/admissions team to advocate for a student-athlete applicant who can contribute in multiple sports and/or extra-curriculars.
I’ve never heard of an applicant being contacted about a sport they haven’t shared they’ve played. But I have heard of kids contacted by a coach once they’re on campus as a student—football/lax crossovers as both teams need more players—and tall, athletic kids for rowing and compact kids for coxswain.
I’d add that if a school is adding, re-building or trying to grow a program those coaches might be looking internally at applicants to help their program? If it’s a school that your child really likes it could help them in the admissions process.