I don’t think it hurts at all to write a thank you note, and it is certainly courteous, but I agree with Soozievt, that they are not necessary. They aren’t necessary for several reasons: It’s their own requirement for getting into the college. You have paid a considerable amount to be there, and they are also doing their job in admissions. Anyway, typically, for stage auditions (in college and beyond) you don’t write thank you notes for auditioning.
My own kids mostly did not write thank you notes - although they were certainly grateful for the opportunity. Again it’s a nice idea, it can’t possibly hurt,but it’s not necessary. I don’t think it’s expected either, just as it’s not expected to write thank you notes to regular admissions committees for the “opportunity” to submit college applications to them.