Karen,
The short answer is yes, but obviously this is not something you can do without manipulating the code. There is no configuration setting that can be changed for this. You would begin by looking at the HeaderControllerWidget and changing the WidgetListDataGroup layout to horizontal instead of vertical, then you will need to change the WidgetListItemRenderer.mxml and comment out the label control and add the tooltip to the icon using the widgetItem.label. Then you have a lot of work to do with the rendering. Hope your ready...