My son acted professionally for many years. Yes you do write thank you notes to casting directors. I mean, you don’t have to, but it’s a good idea.
You don’t write thank you notes for actual auditions, either at the theatre or during open call or during callbacks. I agree with Soozievt that they are definitely not the norm.
Regardless, this is a college audition. My kids have gone through four now–three of my kids have gone to top colleges, and one is going to a top Masters. In only two individual cases did they write thank you notes–both were all day auditions in which they spent significant time with the director of the program. Again I’m not saying it’s a bad idea. It cannot possibly hurt. I’m only saying it’s not necessary. This is an admissions requirement; you are paying; this is their requirement to get admitted to their university. If you send your admissions packet to a regular college, you don’t write thank you notes to the committee for reading it.