That the Ivy league do not provide athletic or academic scholarship is an insignificant distinction. For all practical purposes the need based financial aide is equivalent to an athletic scholarship in the eyes of NCAA, the players, their parents, the OCR (Title IX). Financial aide and athletic scholars cover tuition and fees, room, board and course-related books. It is impractical to make the distinction because the NCAA and Title IX doesn't care. As an example, the roster size limits (players on full scholarship for WBB) is the same for Ivy league institutions as for all D1 institutions. Another example is when a player decides to transfer from an IVY league school (believe it or not there have been some) the NCAA just doesn't say well you weren't on "scholarship" at that Ivy league school so you don't have to sit a year.
From the player's POV the significant difference (advantage really) is in the admissions process. Ivy League schools lack of participation in the NLI signing day is also insignificant. Some Ivy League will send their most wanted prospective athletes a "likely" letter. Although not legally binding it serves the same purpose as a LOI. For the Ivy League school it says you are likely to be accepted based on all the information we have received, as long as you continue to do well. Note: The vast majority of Ivy League students athletes do not receive a likely letter. You can respond to the likely letter and let the coach know that you are coming and this serves the same practical purpose of the NLI.
After admissions there is very little difference between a full scholarship athlete and an Ivy league athlete whose full needs (tuition and fees, room, board, & books) are being met. The Ivy League teams are also given a budget to take care of the teams just like teams at other NCAA institutions. Those budgets included monetary payments to players for things like meals and incidentals expenses while traveling or across summer sessions. These expenditures are subject to strict monitoring by the NCAA and the Office of Civil Rights (OCR).
After graduation the most coveted Ivy League student athletes are in the same position as full scholarship athletes at other institutions-they are debt free and mom and dad will have kicked in very little (if anything) for tuition and fees, room, board, & books over the prior 4 years.
My experience is largely based on WBB and talking to coaches from Penn, Brown, Dartmouth, Yale, as well as Courtney Banghart during her very first summer on the job at Princeton.