The stats I have seen have run at a half. Don't know, however, what exactly they cover in terms of financial aid. You can get Stafford loans and PELL without requesting aid from the schools themselves but it does get processed through the schools so they would know about it.
For most schools it does not help you at all. Most schools are need blind in admissions. They just gap those who have need if they don't have the funds to allocate or don't want to give the amount you show as need. That is the vast majority of schools. Then you have the tiny group that are need blind AND guarantee to meet full need, and those tend ot be the most selective school. Again with them having no need makes no diference for admissions.
There is a small gorup of schools that do take need into consideration. They tend to be highly selective and they are need blind for a high percentage of their applicants, but maybe 10% of the applicant pool are affected by their need aware policies. These schools tend to either meet full need or close to it for those they accept, so they cannot accept anyone and maintain that policy. What they generally do is to overaccept from what they expect they need, and rate the accepted kids, say with a 1.2.,3. Everyone in that group who doesn't need financial aid is accepted. But for those who do need, aid, the names are sent to FA, and the 1s and the 2s get their need met with the best packages, the grants, and then they look to see who they can accept of the 3s. The 3s also will tend to get more self help in their packes. So unless you are in that 3 group asking for aid you are not affected, It's not so much that you get a boost not needing aid but that you don't risk being cut in that last stage if you are in group 3.