Adidas doesn't have the same influence as other schools. And it usually has more to do with top-top-top recruits (like Diamond Stone... who ironically ended up being a bit of an NBA draft bust...). It's not worth the shoe company money, time, or energy, for the companies for kids who may go to the NBA like a MAL, whereas top 5 kids are much, much more likely overall.
I think it definitely depends on the kid. Some are really being influenced by outside sources, maybe the more money hungry kids. Others are more family oriented, or looking for a real college experience. who knows. I hope that UCONN attracts the latter type more.
I promise that sneaker affiliation influencing *not dictating* recruiting is real.