Look at Utah. They were nothing for decades and had minimal fan support. Now they're the top team in the state with tons of fan support and energy. Utah State was beyond abysmal for a LONG time, wallowed in independence due to the Big West dumping football, and struggled to get anyone to come to a game. Yet now they are enjoying success and consistently going bowling.
As badly as things can go, it only takes 1 good season to get people excited. Honestly, it only takes a game or 2. Think how excited BYU fans were after the USC game? It's the nature of the beast. Winning cures all.
As for shutting down the BYU football program, I don't believe that would have much to do with wins/losses. When they shut down football at Ricks, it was one of the top Jr. colleges in the country. Ricks was shut down for reasons that had NOTHING to do with success of the program. If the Brethren decide to do the same at BYU, I doubt it will be because of some losing seasons.