Winning definitely creates recruiting. It's how the blue bloods remain blue bloods. They win because they recruit well, and they recruit well because they win.
It's a perfect chicken and egg metaphor though. People are arguing over which one is the egg.
There are actual rankings for this kind of thing (top party schools), and we are routinely in the top 10 nationally every year. There have been a couple years in the past decade with us at #1. So, no, not "literally every school save a select few" can make the same case we can.