Back to the OP, no one here really knows if full pays have an advantage in Ivy admissions, because none of know exactly if and how financial info/proxies are used in the admissions process. Certainly all 8 Ivies have variability in their admissions processes as well.
The only piece I know is that many coaches know the fin aid status of their recruits and some express positive affirmations if the student needs minimal/no aid. Many of the Ivies will also do financial aid pre-reads for recruits. I expect all of this info finds its way to admissions, but this is a relatively small percentage of the admits.
I’m not sure why you are asking this question, but if you are asking if being a full pay Ivy applicant will minimize the impact/allow AOs to overlook stats or some other factor that is lacking, the answer is it won’t.