Agree with comments above. Financial aid status won’t be a factor at Ivies or other D1s, might be at some D3s.
That’s not to say D1 coaches won’t try to leverage need based and merit aid to stretch their athletic dollars where they can. But they aren’t going to sour on a recruit they want just because they’re full pay.
Whether they’ll offer less because they know you can pay is more difficult to predict. Generally the market takes care of this.