I think many BYU fans would be surprised at how high the fan support already is among BYU-Idaho students. My roommates and I, for instance, traveled down from Rexburg for 3-4 home games a year. The football games were shown in the student center during the MTN days (maybe still are) and were usually well attended.
Playing a basketball game there vs Idaho State would be awesome for BYU-I students and probably go a long way to grow the fan base. Perhaps a Volleyball game or even a frigid baseball game.
BYU-I needs to be proactive as well. There are a lot of students there who love the school and all it offers but resent the fact they do not get to cheer on a team. Seems to me like building a relationship around BYU sports would be beneficial for both schools.