Highly unlikely they get an at-large bid. Though I don't follow much CBB other than UConn, there doesn't seem to be many compelling stories that haven't already been beaten to death. Those 14 loss teams came when there were 6 major basketball conferences. Even when Louisville won in 2013 and UConn won in '14, the AAC has not been treated like a major conference, post Catholic split.
UConn has been pretty exciting lately, but the two comebacks were vs. Memphis and Temple and they got demolished vs. the only good team in the 8 game stretch. The Huskies are going to have to win the AAC Tournament and even then, the committee will not treat them as fans had grown accustomed over the last two decades.