Would a Valedictorian from a non-ranking school get auto admit?

Title says it all.

Will you be declared valedictorian before December 1? How will UT know you are valedictorian?

Chances are you won’t be able to say that before admission deadline.

Here is what UT says:

"However, we understand that some schools choose not to report rank for a variety of reasons. If that’s true for your school, here’s what you need to keep in mind:

When making admission decisions, we consider rank for all applicants, even those who are not eligible for automatic admission.

In recent years, more than half (often a good deal more) of our entering freshmen were admitted based on rank alone. That means that any student who applies without a reported rank (even those at the top of their graduating class) will compete for spaces that remain after all eligible students have been automatically admitted.

Your High School Profile

To help us fairly consider applicants from schools that do not report rank, we ask each non-ranking school to send us a high school profile. We use the information on the profile to help us assign a rank to the students from a specific school. (The University uses assigned rank when reviewing an individual applicant’s file. However, assigned rank cannot be used to award automatic admission.)"

http://bealonghorn.utexas.edu/counselors/hs/policies

the very last sentence answers your question.