Sure they can Lisa. The SCOTUS ruling which eliminated affirmative action in admissions also included this :
"the Supreme Court didn't remove race completely from the application process for higher education because the Court added applicants still have the freedom to "discuss how race affected his or her life, be it through discrimination, inspiration, or otherwise."
"...A benefit to a student who overcame racial discrimination, for example, must be tied to that student's courage and determination. Or a benefit to a student whose heritage or culture motivated him or her to assume a leadership role or attain a particular goal must be tied to that student's unique ability to contribute to the university.
For example, if I were applying to my alma mater, Embry-Riddle Aeronautical University as a high school graduate, I could include information about how my grandfather having been a Tuskegee Airmen during a time when the U.S. military was racially segregated inspired me to want to follow in his footsteps and pursue a career in aviation as a commercial airline pilot. After WWII the airlines still refused to hire Black pilots even those with such outstanding and impressive records as the Tuskegee Airmen, some of whom were denied entrance to an officer's club due to being Black. It was also reported that German POWs were treated better than the army's own Tuskegee Airmen simply because the German prisoners were white. Imagine that, white American racist who identified more with Nazi Germans than their "fellow" American Black pilots, who often protected them during combat.
As it turns out, I was accepted to and graduated from the only university I wanted to attend and had applied to which was Embry-Riddle. I don't remember specifically being asked about my race and since I didn't learn about the Tuskegee Airmen until after I was enrolled as a student there I couldn't have used my grandfather to make my application more desirable back then.
Honestly, how or why I was accepted was never something I gave any thought to until I had the misfortune of encountering a bunch of racists on the internet who have always insisted that the only reason I have achieved anything in my life is due to affirmative action and all at the expense of one or more, more deserving and thus deprived white males.