@twoinanddone,
Quick search shows, for example,
http://www.athleticscholarships.net/2013/09/12/how-financial-aid-trends-affect-college-athletes.htm
"In general, when need-based aid is combined with athletic scholarship dollars, the need-based aid counts as if it were athletic scholarship. "
So it seems if the NCAA sport is underfunded there are opportunities to award need-based aid.