If you google the stats, or check collegedata.com, you can see the makeup of a college’s ethnic population and make some (right? wrong?) assumptions about where race might place you.
I agree with @thumper1 that I’m not sure what good it might do to check that box given your special circumstances. My daughter is only a junior - and is a Chinese adoptee - so it remains to be seen what that means for her since many of her target schools have Asian populations in the low single digits.