FWIW, the Big East's contingency plan with the Liberty Bowl is more dependent on what happens with the SEC. If the SEC doesn't have enough bowl teams to fill the BBVA Compass Bowl, then the Big East team that would normally go to the Compass Bowl goes to the Liberty Bowl to play an SEC team there and Conference USA can send their champ to one of their other bowls, and a Conference USA team would also go to the BBVA Compass Bowl. If the SEC doesnt have enough teams for Liberty or BBVA, then the Big East team plays CUSA champ in the Liberty, and Compass has to go to contingency picks.
That said, NCAA has never done contingency picks well. Notre Dame has always had an affiliation with certain Big East affiliated bowls, notably the Gator in the past, and I remember one version of NCAA where Notre Dame went to the Gator Bowl 5 straight years in a dynasty.