I can see an underachieving football team causing a school's fan base to show more interest in the basketball team in early November.
I also remember a time when the financial failures of a UNLV football team caused the UNLV basketball team to bus, not fly, to a game in San Diego.
Some football teams, like Duke and Michigan State, use basketball games to recruit football players.
And, of course, the athletic/academic culture is usually the same for a football or basketball player at a high-profile university.