Not really. Morning Musume never had strong staying power. They are a group geared towards an otaku fanbase, and while that is a hardcore fanbase, the groups catering to it are not going to be loved by casual music listeners, or "normal" people.

A lot of really popular bands and singers in Japan have had a lot of staying power;
Mr.Children, BUMP OF CHICKEN, Yuzu, SOUTHERN ALL-STARS, etc.
They're the kind of bands that appreciated by people of all ages because of their music, not because they have cute, underage girls.