Glad you gave me a chance to dispose of wives tales like the "national champion" vs. application myth. Scholars have tested it repeatedly and found no evidence to support it. What you may be referring to is the "Doug Flute" effect, when the short QB lofted a hail mary back in the 1980s that his brother somehow grabbed from a crowd of defenders to beat, ironically, UMiami. I watched it live (it was at 4:30 in a December bowl game on a Friday), but guys like to claim they saw it. Application to BC did surge for a year or two, the only exception. And BC is famous for being the "safety school" for Ivy applicants -- not exactly something they want to be known for.
The attendance to winning percentage relationship is a relatively weak one in college and getting weaker. How weak? Multivariate statistical studies find win% is one of the weakest factors, and not even statistically significant. What does matter for football or basketball attendance? Number 1: residential colleges get much, much higher attendance because they have a captive audience of students, a shared full-time bonding experience, alums returning to campus to renew that identity. Number 2: (especially for basketball) private colleges have no time conflicts -- half of students don't even apply for financial aid (not that they'd qualify) and most don't need to take part-time jobs [half my students work full time]. Number 3: Age of the college which also serves to measures tradition, reputation, alumni donations, legislative funding, etc. Number 4: Enrollment. Number 5: size limit of the arena or stadium.
Why doesn't winning affect attendance much? Pre-season season ticket sales dominate established university attendance, so only last year's W-L record could affect ticket sales. But that doesn't occur either because if you don't buy one year, you lose your existing seats and an opportunity to improve them in future years -- you go to the back of the queue. In addition, most of the expensive seats are not occupied but the purchaser. NHL games, for example, have most of the better seats given to clients (that's how I've always gone to Magic and St. Pete hockey games). These are tax deductible entertainment expenses. Or civic and business buy up the always-empty $5000 seats on the player bench side of UCF games. Students pay $14 for each football or basketball game whether they show or not (most don't, of course) in the form of their student athletic fee, one of the highest in the nation, but students won't show unless you give them some worthless toy or walking advertisement apparel.