The question is self explanatory. Rather, I should specify two questions: do they say they do, and/or do people suspect them of doing so?
They do collect and report this data, although that seems more for their own reporting than for stuff sent to colleges.
https://research.collegeboard.org/about-us/changes-to-race-ethnicity-reporting
Perhaps it’s best to check to see what’s included on the Score Report sent to colleges.
It’s also best to make sure your ethnicity information lines up consistently for all this stuff since you are not sure exactly how it’s being used. Among other things, you wouldn’t have to have any nagging worries about what boxes you checked and when.
The language in the link above, “Test takers now complete a two-part question that asks them to indicate their racial and ethnic group,” suggests to me that responding to these questions is not required.
Is there something compulsory in the language written in the exam booklet, or the instruction by the proctor? Is there an opportunity to opt-out?