I am not sure if this A MAN OF NO IMPORTANCE would fall under the classification of a Broadway "revival", as the original never ran on Broadway.
The 2004 Assassins was considered a revival, only previously having played its limited 1990-1 run at Playwrights Horizons. The 2004 Little Shop (its first time on Broadway) was nominated for a best revival Outer Critics Circle award. (I don't know if the Tonys considered that production a revival or not). I imagine there are others that also have set that precedent.