My personal opinion is that colleges know the demographics of high schools whether or not they are need blind or not. At the end of the day, colleges are big business and they need to make sure that they don’t accept a class of 100% full financial need based freshman.
I’m most cases, being full pay is a positive for the colleges. For example, full pay close friend of D’s was given spring admit At BU with less than stellar grades and test scores. I’m pretty sure her full pay status got her an acceptance.