Beginning with ArcGIS 10.1, no; feature classes added to feature datasets inherit the privileges set on the other feature classes in the feature dataset.
For ArcGIS 10 and previous releases, yes; when adding a new feature class to a feature dataset in ArcGIS 10 or earlier releases, the owner needs to re-grant privileges to other users for the users to view and/or edit the new feature class.
If the privileges are not re-granted in ArcGIS 10 and previous releases, the privileged viewers are not able to view the newly added feature class; they can only view the pre-existing datasets. In cases where the feature dataset was registered as versioned, the editors can no longer edit the contents of the specific feature dataset. Upon starting an edit session on any of the available feature classes of this feature dataset, the following error message displays.
Error: Could not edit any of the map's layers. No data sources in the map are registered as versioned or you lack privileges to modify data sources which are registered as versioned.
To re-grant privileges, follow the steps outlined in the following Web Help topics.