It depends. The admissions committee at Caltech might care if a PhD candidate from another country won the contest.

However, Caltech itself doesn't care that much about its team's performance.

UCF is a great example and one that I'm familiar with. UCF has a faculty member that's very involved in their programming contest program. That brings a lot more consistency, probably a little money, makes it easier to recruit students, etc. They have a great library of problems to practice on. They also run a high school programming contest which helps identify talent and recruit, but also helps get more UCF students involved.

When I was at nearby USF, our programming contest teams were student-run. It's not a priority for the department and there is a lot of inconsistency as students come and go. There's also a smaller pool of participants to draw from. We did reasonably well for a little while when I was there and put a bunch of time into it, recruiting, teaching, running practices with and without other unis. But it takes a lot of effort.