I think it depends on how we define "classic". In 1997 the band Days of the New was #1 on Billboard Mainstream Rock for 16 straight weeks.. Not sure we consider them a classic though..
I feel fun. will be similar.. Those that are in the scene that knew of them prior to their exposure will continue on and think of them as classic, whereas true mainstream (with their short attention) will move onto the next fad..
Just my opinion though