As other posters have said, the key is Hageman. If he can be dominant (I realize that's a big IF), it shouldn't be nearly as much of a problem. If he plays like he has shown flashes of, he will need to at least be double teamed.
Botticelli needs to continue to improve. I liked him more last year than other people.
However, other than that, I think your concerns are valid. This is the area of the game that concerns me the most (even more than our passing game). I never thought that Rallis was an overly physical OLB and now he is in the middle. I like Cooper, but I think he's better in space than he is in the box. We don't have Royston now, and he was our best tackler last season and he made a lot of plays in the run game. Our DE are young and talented but they aren't huge and they are more focused on the passing game (by design). In fact, I think our best two players against the run last season were Royston and Tinsley, and they are both gone.
There are a lot of "ifs" in a scenario that involves us having a lot of success running the football (if Rallis has a real good year, if Rallis stays healthy, if HAgeman is healthy/consistent, if Botticelli improves, if Wells/Vereen step up and tackle as well as Royston).